brain memory,mental image,imagination,equimerec

Mental Image

This website is adressed to people working in two different but related domains. The nature of the menal image is probably interesting to researchers of : neurology, neurophysiology, neural sciences, neuro-psychology, cognitive sciences, psychology and psychiatry.

The action of human memory is important also for people considering problems of artificial intelligence, robotics, automatic translations and virtual reality. This page contains two papers which are in print in conventional scientific journal. It is an English part of larger website devoted to neuro-psychology (structure and action of the brain) accesible here

The actual content of the page 1.Neurophysiology of the mental image 2.Model of Neural Circuits Recalling the Mental Image

Laboratory Investigation Med Sci Monit, 2001; 7(3):

Neurophysiology of the mental image

Andrzej Brodziak Department of Internal Medicine, Silesian Medical University, Bytom, Poland

key words: mental image, memory, imagery, brain, electrical activity, electromagnetic field

SUMMARY

Apart from perceptions, mental images are the most frequent experiences of the conscious mind. Mentation can be understood as a process which consists in the manipulation of recalled or imagined mental images. The scientific literature related to this process is relatively scant. This article reviews the relevant original and recent neurophysiological data in such a way as to enable the presentation of a synthetic theory of the neuronal mechanisms that form mental images. Recurrent axons and some reproductive efferent connections constitute the neural circuitry essential for imagery. These connections enable the reverberating, circular arousal of the upper levels of the hierarchical structure active during previous perceptions. The recalling of a mental image evokes an accompanying electromagnetic field. The investigation of its functional role is a challenge for contemporary neural scientists. BACKGROUND

Perceptions and mental images are the most common experiences of the conscious human mind.Mental images are probably experienced more frequently. The recalling of a mental image is the starting point for mentation. Mental activity typically consists of imagined manipulations of recalled mental images.

Sometimes the product of mentation is the imagination of an object which did not previously exist.This is necessary for creativity. Self-awareness is based on the ability to recall images from oneOsown past experiences, and images of oneOs ownbody and person against the background of pictures of the world. Constant recall of mental images is probably one of the essential characteristics of the human mind.

The understanding of the neurophysiological mechanisms of known and remembered objects, as well as own present and future (desired) situations is an important factor for the improvement of psychotherapeutic techniques. The theoretical basis of the neuropathology of the imagination is important for the understanding of schizophrenic disturbances of thinking and other mental diseases. Moreover, the knowledge of how to reproduce imaginary processes in artificial neural networks would make it possible to construct Ôartificial thinking systems.O This would most likely constitute the next step in the development of so-called artificial intelligence and robotics.

These important possible consequences of a better understanding of the neural mechanisms of mental image formation provided the impetus to undertake this review of some of the relevant recent neurophysiological data, and to draw some synthetic conclusions.

The number of scientific papers related to mental imagery is comparatively small. Surprisingly enough, until rather recently the existence of mental images was not scientifically recognized or investigated, until chronometric psychophysical measurements were performed of the possible speed of rotation of imagined objects [1]. The study subjects were requested to determine whether two patterns presented in turn at a different angular orientation have the same shape or a mirror-image shape. These experiments proved the real existence of mental images.

The mechanisms of mental image formation should be described on the basis of the functions of neurons, and the structure of the circuits responsible for realizing perceptions and recognizing known, remembered objects. It would also be useful to review data related to long-term and short-term memory. It seems clear, also, that a comprehensible, synthetic theory of the mental image should be based, not only on the most recent data, but also on certain facts and insights already reported many years ago.

THE FUNCTION OF THE NEURON

The neuron, like any living cell, maintains the electrical potential gradient between the inside and the outside of the cell. A negative load inside the neuron is created by the so-called active transfer of sodium ions on the outside of the cell membrane.Impulses reaching the neuron through the synapse cause a decrease or increase of the resting negative gradient of the neuronOs electrical potential. When the neuron receives many impulses within a short period of time, the threshold is crossed, after which the action potential is generated on the axon of the neuron. The term 'action potentialO refers to the gradient of the electrical load transferred along the axon and its dendrites to the neurons of the next layer. When the action potential reaches the synapse with the next neuron, the quantum portion of the neurotransmitter is stimulated, which changes its resting potential. According to HebbOs rule [2], the frequent activation of the neuron and its synapses causes functional changes in these synapses: they become more effective, and their data-processing 'weights' increase.

THE NEURAL CIRCUITS REALIZING PERCEPTIONS

After the learning period, the neuron is sensitive to a particular pattern. For instance, if the weights of the synapses in the central region of the body of a neuron are increased, while the circumferential synapses are not changed, the neuron will be sensitive to a dot pattern. Stephen Kuffer discovered neurons of this kind in the ophthalmic retina [3].

Figure 1. The visual pathway extends under the projective occipital field and then turns towards the anterior part of the temporal lobe.

David Hubel and Torsten Wiesel, in a series of famous experiments, proved that at higher layers of the visual integrative pathway there exist neurons sensitive to more and more complex patterns [4,5]. The lateral geniculate body and the striate cortex contain neurons which are sensitive to rows (lines) positioned at different angles in the visual field. At the next layer, then, the crossing of lines existing in the visual field can be detected.

Advocates of the existence of the so-called 'gnostic' neurons, which represent particular known objects, such as an apple, an orange, a chaise lounge, a table, a face, and so forth, have been engaged for many years in a dispute with the adherents of more diffuse models of neural struc- tures. The idea of such high level 'gnostic' (object) neurons was first proposed by J. Konorski [6]. The experiments of C. Gross and M. Mishkin seem to have proved that the neurons located at the highest points in the neural architecture represent objects important for humans [7D9]. These are located in the anterior part of the temporal lobes.Thus the visual pathway does not end in the occipital region, but is prolonged by superior structures placed above the occipital lobe. From the anatomical point of view, the visual pathway is bent, aiming towards the anterior part of the temporal lobe.This is illustrated on fig. 1. It turns out that the idea of 'object neurons' is not in fact inconsistent with the diffuse model of data processing, because any given object is represented by many such highestlevel neurons, which constitute a set of multiple representations of the object [10]. Parallel processing is also realized by structures representing different aspects of the same object, such as shape,size, color, or texture.

The occipital cortex is a kind of a 'space-volume modeling processor' [11,12]. This means that the activation of many neurons comprising short segments inclined at different angles relevant to the horizontal plane reproduce here a three-dimensional replica of the external world.

Figure 2. The cooperation of two separate loops is necessary to realize short-term memory traces, and sometimes long-term as well.

This replica reproduces distances and other topological and relational characteristics of the observed fragment of the external world. According to Shepard, this 'space-volume modeling processor' utilizes Rieman's geometry, rather than Euclidean, and does not reproduce inertial phenomenon [12].

THE NEURAL LOOPS CONSOLIDATING MEMORY TRACES

In the late 1950s, Wilder Penfild stimulated the cortex of conscious patients during brain surgery for epilepsy performed under local anesthesia [13]. The patients reported vivid experiences of past events. He also demonstrated the existence of language 'object neurons.' A written or pronounced word is of course also an object [10].

Brenda Milner found that neurosurgery performed on the hippocampus caused a profound and irre- versible deficit of recent memory [14]. Patients lost the capacity to form new long-term memories, but previously acquired long-term memories remained intact. It was later discovered that some hippocampal neurons exhibit Ôlong term potentiationO. This means that their resting potential is almost steady near the threshold of activation. If such neurons compose a loop with certain cortical Ôobject neurons,O the circuit can easily fall into oscillations. The phenomenon of self-sustained, repetitive oscillations after the activation of a gnostic neuron is important for the consolidation of memory traces.

The neurosurgical experiments performed by Mishkin on monkeys, however, proved that two separate but cooperating loops are involved in the mechanism of long term memory [8].

Figure 3. Long term memory traces exist not only due to changes in the synapses of afferent pathways, but also due to the adjustment of ÔweightsO in efferent reproductive connections.

This can be seen on fig. 2. The first loop, based on the previously-described loop with hippocampal neurons, is necessary to maintain the arousal of a mental image activated from the speech area or by the operation of another mental process. These loops are essential for short-term memory. The second kind of loop involves neurons situated in hypothalamic structures, especially in the amygdala nuclei.Hypothalamic and limbic structures are known to be centers of emotional phenomena. The activation of the cortex-hypothalamus (limbic) loops is necessary for the consolidation of memory traces,leading to the formation of long-term memory.

The morphological and biochemical characteristics of durable, long-term memory traces have been thoroughly investigated. E. R. Kandel, who experimented on the Aplisia californica snail, demonstrated that the learning process causes a morphological change in the synapses of neurons forming the structure that recognizes a frequently perceived pattern [15]. Gary Lynch found that the calpain enzyme acts during learning on the membrane protein fodrine and changes the shape of the synaptic butt [16].

THE NEURAL CONNECTIONS NECESSARY FOR RECALLING MENTAL IMAGES

It is known that many cortical neurons have socalled recurrent axons. This was demonstrated as early as CarpenterOs histological pictures of the cytoarchitecture of the cortex [16]. These ramifications are necessary in order to activate the lower levels of the hierarchical structure at the moment of the stimulation of a gnostic (object) neuron from the speech area or during more complex mentation. When the neuron of a known object is stimulated, next, the activation returns D by means of recurrent axons, or more generally by reproductive pathways D to lower levels of the hierarchical structure constructed formerly during perception and the learning process. This is illustrated on fig. 3. Downward activation can even proceed to a lower projection level, such as the occipital cortex, causing vivid dreams or hallucinations.

It is important to note that the structure which during the learning process is ÔtunedO to recognize a particular object reinforces not only the synapses of the afferent pathway, but also those of reproductive connections. This is also shown on fig. 3.

When such a structure is activated from below by repeated perceptions, the gnostic neuron is further stimulated by the cortex-hippocampus indexing loop. Thus the structure of a known object is stimulated from two directions. When the object neuron is stimulated from the speech area, the mental image is recalled. The neural mechanism of the mental image consists in the circulation of impulses up and down along superior levels of the hierarchical structure, which is maintained by the cortex-hippocampus indexing loop. It has been demonstrated by the present author and co-workers on an algorithmic model that such reverberating activations last for a measurable period of time [17].

Upon activation by a known, previously memorized pattern, the neuron generates action poten- tials with a frequency of 300D500 Hz. Any spikes that may occur are gradients of 100 mV translocating along the axon and its ramifications in a wave form at a speed measurable in m/sec. When we take into account the fact that the activation is proceeding along a circular path, it should be apparent that, apart from this Ôelectrical shape,O a magnetic field is also formed, which in turn suggests that any image in the imagination has an Ôelectromagnetic shape.O One of the most intriguing questions is whether this electromagnetic field of the mental image is only a byproduct, or plays some functional role.

RECENT FINDINGS RELATED TO THE ELECTROMAGNETIC FIELD OF THE MENTAL IMAGE

Methods enabling the examination of certain aspects of the electromagnetic field of the mental image have been developed only recently. The specific activity of particular regions of the brain during the mental rotation of an imagined object was first confirmed by the evoked potentials method [19,20]. Later, this particular neural activity was revealed by positron emission tomography [PET] [20] and functional magnetic resonance imagining [fMRI] [22D24]. It was also discovered that different mental tasks are characterized by a specific spatial distribution, determined by mapping the brainOs electrical activity [25]. A characteristic change in the magnetic field during the rotation of an imagined object has also been detected directly by magneto-encephalography [26]. It would appear that, as previously predicted, the mental rotation of an object is accomplished by means of those same neurons situated in the motor areas which realize the corresponding real movements [27,28]. Some physicists have postulated that the non-local quantum effects of the pulsating electromagnetic field should be considered [29]

CONCLUSIONS

It remains unclear whether the activation of additional regions of the brain (often the parietal lobe) during the mental manipulation of recalled mental images (such as rotation or linear transformations) changes the replica (reactivated pattern) aroused in the primary projective fields of the brain, such as the occipital lobe [30].

There are theoretical arguments in favor of the hypothesis that the electromagnetic field accompanying the formation of the mental image has some functional meaning. For instance, mentation directed to problem-solving should entail a comparison of the images of the actual and desired situation. According to the theory, the possible intermediate steps leading from the actual to the desired situation, when imagined, should cause double activation of the corresponding neurons involved in such mentation. This double activity can direct the search for a solution.

A search for structures indicating increased electromagnetic activity would be justifiable. The investigation of the functional role of the electromagnetic fields accompanying cerebral activity is a major challenge for contemporary neural scientists. These investigations should probably begin with the construction of appropriate circuitry models in artificial neural networks. If the theory of neural mechanisms of mental image formation presented here is valid, it should be possible to produce relatively simple simulations of equivalent phenomena in technical systems.

REFERENCES:

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9. Mishkin M, Appenzeller T: The anatomy of memory. Scientific American, 1987, 6

10. P A neurocybernetic model of image processing. Aphasiology, 5: 447-450

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15. Kandel ER: Cellular basis of Behavior. An introduction to behavioral neurobiology. Freeman, San Francisco, 1976

16. Kandel ER, Schwartz JH: Principles of Neural Sciences, Elsevier North Holland, 1981

17. Lynch G: The biochemistry of memory D a new and specific hypothesis. Science, 1984; 229: 1057-1060

18. Brodziak A, Rya M: The unit of neural networks modeling recall of mental images by oscillations of feedback loops, caused by change of set-point signal. Problemy Techniki w Medycynie, 1990; 2: 30-37. Text of the paper accessible also under: http://salve.slam.katowice.pl/phenomen.html

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22. Foster BB, MacKay AL, Whittall KP et al: Functional magnetic resonance imaging: the basis of blood oxygen-level dependent (BOLD) imaging. Can Assoc Radiol J, 1998; 49: 320-329

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24. Barnes J, Howard RJ, Senior C et al : Cortical activity during rotational and linear transformations. Neuropsychologia, 2000, 38, 1148-1156

25. Lehman D, Strik WK, Henggeler B, Koenig T, Koukkou M : Brain electric microstates and momentary conscious mind states as building blocks of spontaneous thinking. Int J Psychophysiol 1998; 29: 1-11

26. Iwaki S, Ueno S, Imada T, Tonoike M: Dynamic cortical activation in mental image processing revealed by biomagnetic measurement. Neuroreport, 1999; 10(8): 1793-7

27. Olivier G, de-Mendoza JL: Motor dimension of visual mental image transformation processes. Percept Mot Skills, 2000; 90(3): 1008-26

28. Ruggieri V: The running horse stops: the hypothetical role of the eyes in imagery of movement. Percept Motr Skills, 1999; 89(3): 1088-92

29. Pitkanen M: Brain as a macroscopic quantum system. [http://www.physics.helsinki.fi/~matpitka/newcbook.html]

30. Koriat A, Norman J: What is rotated in mental rotation? J Exp Psychol Learn Mem Cogn, 1984; 10: 421-434

Received: 1999.01.18

Accepted: ?????

MODEL OF NEURAL CIRCUITS RECALLING THE MENTAL IMAGE.

Andrzej Brodziak e-mail : andrzejbrodziak@wp.pl

KEY WORDS mental image, memory, brain, neural circuits, reverberating circuits, equimerec unit

SUMMMARY

Introduction Consideration of structural and bio- molecular mechanisms of neural memory should encompass also data processing rules of the neural circuits. The author try to find the concrete physical and mathematical meaning to the process of recollection from memory in neuron like-element networks and to the related notion of mental images. They deduce the nature of this process from old concepts of homeostasis and self-control (feed-back loop) and memorization of data by synaptic weights of threshold logic units.

Material and methods The experiment consisted on the simulation of data processing performed by an artificial network composed from feed- back loops and threshold elements reproduced on a computer.

Results The author found simple but extendable unit, which can keep equilibrium, memorize data, recognize an image and recall it in the absence of the external object. He try to coin the term 'equimerec unit' for this kind of neural networks. He verified the functional consistency of this elementary unit through its simulation on a computer. A simple mathematical analysis is also presented. The defined unit has back-propagating connections, which transmits set-point signal. The authors quote neuro- physiological evidences supporting this model of reverberating circuits and reverberating excitations.

INTRODUCTION

Most of investigations related to neural circuitry consider anatomical, biochemical and bio-molecular carriers. Neural networks should be characterized however also by comprehensive data processing rules.

The basic elementary mental process related to the memory consists on the recalling of mental images. Mental images , apart from perceptions are our most frequent experiences. Mental activity consists usually on imaginary manipulations on recalled mental images.

Some neuro- physiologists emphasize the meaning of so called reverberating circuits and reverberating excitations as mechanisms underlying the dynamic, short- term working memory ( 1- 10 )

Principles of neural memory are different from other memorizing systems. Elementary steps of the memorizing and recalling should be therefore determined and explained.

It is approved already that the imagination consists on arousal of the same structure, which was active during the perception ( 9,10 ). This structure should be activated, in the case from the side of so called associative connections. Afterwards, upper levels of the hierarchical structure are activated due to so called recurrent axons and reproductive pathways ( 1, 9 ).The mechanism of reverberating excitations occurring in such neural circuits should be explained.

The signal coming from the speech area, through associative connections is usually short, caused by the read or pronounced word or other presented symbol. The imagination of the object denoted by a symbol ( word ) last however some period of time. It is due to the mentioned reverberating excitations. We propose a simple, comprehensible model explaining the mechanism of initiation and shorter or longer lasting of the reverberating excitations.

MATERIAL AND METHODS

Our experiment consisted on simulation of data processing performed by an artificial network reproduced on a computer. The essential part of our methods arise from search for appropriate formalism suitable to depict the data processing of a reverberating neural loop.

Recall from memory is a very basic process, which is probably related directly to yet more primary concepts explaining the phenomena of self - control. Therefore we try to combine the basic concepts of biological homeostasis and self-control ( 11,12 ) with the oldest concepts of a memorizing unit, it means the threshold logic unit ( 13 )

Comparison of the outline if the threshold logic unit ( fig.1) with another, old known notion of the feedback loop (fig.2 ) reveals that they are related to each other. However both original outlines are incomplete, in some sense, because the first doesn't say what signifies the mysterious element - w_n+1 in the formula describing its action and the second doesn't precise the source if the set-point signal.

It seems that both concepts are fragments of a larger, more natural system, which are able to keep equilibrium, memorize data, recognize the image and recall it. We propose in figure 3a the outline of such a larger equilibrating-memorizing-recognizing and recalling unit (in short the equi-me-rec unit). Essentially it is composed of two layers of interconnected feedback loops. External influences or external stimuli: x₁, x₂, ..., x_i , ..., x_n, act on lower level elements, which are "under control". The output signals of these elements y₁, y₂ ... act as "influences" (or stimuli) on the element of the higher level loop.

The output signals are compared here with the thresholds T_1A, T_1B, ... It is realized by parts "originating" from the threshold logic units. Similarly, the resistance's or weights of inputs of stimuli can be inserted here also on the basis of our initial intention to make an exhaustive assemblage of two old concepts. The control theory foresees also that the output signal, which is directed back to the input, can be transformed in a different way in "k" or "l". So the signal, returning to the lower subunits can be transformed in a similar way in t and/or p. The most simple transformation of cause is change of the sing f ( s )= - s. Thus, the "error signal" ( e ) , as it is named by the control theory can be :

e = f ( s ) - f ( y ) = - s - f ( y ) = - e = s + f ( y ) (1)

The element under the control can be supplied by a stable level of energy and after the change of the error signal, changes of the output signal in time can have inertial or oscillatory character.

The essential feature of the equi-me-rec unit consists on its ability to fall into oscillations as the result of the change of the set-point signal. If we will roughly discern two values of the set-point signal, coming from a higher level (s): a lower one: s = 0 and a higher one: s = 1, where 1 will be near to the threshold value, and the unit will transform the output signal according to the formula (1), then even in the absence of stimuli x₁ ... x_n, setting s = 1 will cause that e = s + f (y) = 1 + 0 = 1, so it will take a relatively big value and the threshold can be surpassed. The upper subunit will be re- stimulated. Re- stimulation will cause oscillations. Of course, in the situation that s = 0, appropriate amount (or appropriate set) of stimuli x₁ ... x_n can give the same result. Thus the equi-me-rec unit can be activated to a high value by two ways: 1) by external stimuli or 2) by change of the set-point signal.

The system, presented in fig. 3, could be simulated in different, sophisticated ways, assuming binary or continuous - nonlinear character of its components. We conceived however a very simple method, which aims only to check the functional consistency of the concept of the equi-me-rec unit. A very simple model, comprehensible intuitively by any neuro- physiologist would be useful also to promote searching for an appropriate intra - cellular metabolic, molecular mechanisms of its components.

For this purpose it is sufficient to simulate subunits of the system by procedures of one of the object oriented programming languages and use the discrete recycling.

The neuron-like element conceived as a threshold unit only could be rendered in an object programming language by the procedure like:

NEURON -LIKE-ELEMENT 1A

INPUT x₁, x₂,...x_i...x_n

I = ? x _i* w _i

IF I > T_A [ y = 1 ] [ y = 0 ]

END

We formulated the program enabling us to compose and manipulate the system of elements outlined by the fig. 3. The program is written in Logo language and executed using Logo interpreter. Our program illustrates the performed communications among procedures and resulting states of the system by a dynamic outline presented on the screen. The program is available from
http://e-learning5.webpark.pl/equimerecunit.htm

Connections among subunits ( neuron-like elements ) and values of "synaptic weights", as well as values of elements: w_n+1were changed during experiments. We have searched for an appropriate place in the structure presented on the fig. 3 to be able to reproduce in our model so called "associative" connection ( stimulation ) coming, let as say, from "speech area" (see also fig. 4 ). The signal given through such "associative connection" should poke the structure and cause the oscillation of the circuit. It would be the model of so called "reverberating excitations". We verified some versions of possible organization of the equi-me-rec unit.

RESULTS

Finally we found that a consistent, working structure of the unit can be obtained when: external; "associative" signal is given trough the input ( s'' ) and the value of the imposed set-point signal ( y _n+1) decreases in a stepwise manner during subsequent cycles of actions.

The values of the set- point signals: low ( 0 ), medium ( 1 ) or high ( 2 ) are given through the input s". When s" = 0 or s"= 1 or s" = 2 it simulates the situation that a low, medium or high value of the set-point signal was given. The value of the signal is memorized in a 'normalized' scale ( y_n+1) in the element S'. It is assumed that the element S' performs the function R = y_{n+1 *}v_n+1, it means multiply the 'immanent value v_{n+1 '}( see discussion ) by a given, actual value ( y _n+1) of the set-point.

In this case the procedure, reproducing the action of the superior neuron-like-element, has the following form:

`NEROUN- LIKE- ELMENT 2C`
`IF s'' = 0 [ y_n+1= 0 ]`	`(2)`
`IF s'' = 1 [ y_n+1= y_n+1 * g ]`	`(3)`
`IF s'' = 2 [ y_n+1=1 ]`	`(4)`
`I = Sigma y_i * v_i; from i =1 to n`	`(5)`
`R = y_n+1 * v_n+1`	`(6)`
`E = I + R`	`(7)`
`IF E > T_2C [ S=1 ] [ S=0 ]`	`(8)`
`IF R > T_2C[ S=2 ]`	`(9)`
`y₁... y₂ ... y_n =0`	`(10)`
`s₁... s₂ ... s_n =0`	`(11)`
`END`

Please remark that the values given for the elements of the vector S are values s₁... s₂ ... s_n , it means denote the change of the state of memorizing elements of the neuron like elements of the lower level of the network. The procedures, equivalent to the lower-level neuron-like elements are similar and they input y₁ = 0 or 1.

We searched during our experiments for the solution, which would satisfy the main requirement that equi-me-rec unit that it has recurrent features, it means that is could be expanded to a much larger system by the simple addition of next layers. We searched for a structure of the subunit " equi-me-rec" , which could always be the same in a very large network .

The reader should remember here also that the changed set-point signal can come not only from upper layers but, as we call here through "an associative" connection, what means that it come from other part of the network, which can memorize symbols of considered patterns. To emphasize the need of symbols it is useful to remember here the biological analogy of "the separate area pf the brain cortex" which memorized words (Brock's and Wernicke's areas) denoting objects ( its mental images ).

The results of our experiments consist on the proposition of the organization of the equi-me-rec unit. Its structure can be depicted in the form of the fig. 3, where elements A, B, C are characterized by the equations ( 2-11 ). Coefficient "g" in the equations ( 3 ) should be rather small (e.g. 5/6) and the value of threshold T lower then v_n+1 (e.g.: 2/3 * v_n+1).

Oscillations of the unit can be induced through the change of the (s'') signal, but not through the possible input "q". Elements S₁, ... S_i ... S' should have memorizing characters and, as in other inputs, the values immanent for these subunits : w _n+1 , w _d+1, v _d+1should be discerned from the values x ^1A_n+1, x ^1B_d+1, y^2C _n+1 which change during subsequent cycles. It appears that consistent working structure of the equi-me-rec unit should assume two levels of "internal energy" ( " arousal of neuron - like-element), what is represented in equation (7) by a value of "E". Also two levels of positive output (at least two frequencies of "firing") should be assumed. Thus, to the "recognition" of the pattern its "imagination" is attached (equations 6,7) and it causes the double energy (" arousal ") of the system. The activation of the system through "associative" connection (through the increase of the set-point values") cause the similar action of the network, but at lower level of "arousal". We coun'd find other working, consistent structure avoiding double level of "internal energy" to realize changes of weights during learning periods, according to the principle of Heeb . It was not however the aim of our experiment.

DISCUSSION

Mathematical interpretation of our finding can be formulated in terms of the multidimensional geometrical model of the pattern recognition ( 14 ). The activation of the threshold logic unit is an equivalent to the recognition of a multidimensional geometrical model of the pattern ( 14 ). The training, of the threshold element consists of adjustments of weights: w₁ ... w_n . A set of values x₁ ... x_n determines a point in a multidimensional space and also a vector X ( 14 ). Often the similarity of images is expressed by the Euclidean distance among its representing points. A class of similar objects is often represented by the so called mean pattern P_j, it means also a vector, in the same space. It is known, from the geometrical properties of Euclidean space, that the distance between a given point X and a point P_j is expressed by the formula:

________________

? |X - P_j| = ( X - P_j) * ( X - P_j) (12)

The same classification is obtained comparing the square of the expression for the distance:

|X - P_j|²= ( X - P_j) * ( X - P_j) = X*X - 2X * P_j+ P_j * P_j (13)

The fragment X * X doesn't change the classification either, so it can be omitted and we can compare finally only the expressions

X * P_j - 1/2 P_j * P_j (14)

After the learning procedure, elements p_ij = w_ij It means that the elements of vector P_j are equal to so called "weights of resistances" for input signals. As we remember, the vector P_j denotes the learned pattern image. But from the other side, it can be written that:

w_n+1 = - 1/2 * P_j * P_j (15)

The last expression signifies that the value (w_n+1) is determined well by elements of this particular mean pattern, which is recognized by a given threshold element. We have argued above that a high value of the set-point signal is an equivalent of the element ( - w_n+1) and it can replace external signals ( it means the value X * P_j) and causes the transgression of the threshold, which will induce oscillations of the equi-me-rec unit. But as we have demonstrated, a high value of the set-point signal in an equi-me-rec unit denotes the memorized mean pattern of this particular unit. So we can say, that by means of the change of the set-point signal we induce the "home", immanent pattern, which specifies the unit.

Of course the same inference is valid for all neurons. So instead of - w _n+1 we should consider - v _{n+1 ,}enumerated in the equation ( 6 ).

Cognitive scientist Roger Shephard researcher of internal representations of objects and imaginative information processing, found the metaphor of "resonant systems" or "resonance phenomenon" very useful ( 7, 8). However he doesn't consider the physical structures of such circuits. Rumelhart, Kohonen and Grossberg researchers of artificial neuron- like networks , presenting their concept of "back propagating errors" didn't consider problems of recollection or mental images ( 15, 16, 17 ). Thus, it seemed to us important to try to determine structural systems, modeling neural circuits, which have the intrinsic nature to fall into a resonant oscillations, with non-linear changes of states of subunits.

Biological analogy of the defined circuits exists. Some histological (cytoarchitectonic), neurophysiological and clinical data indicate, that so called recurrent axons, and more generally, recurrent pathways, are essential for the process of recalling of mental images and subsequent imaginative information processing ( 1-10 ). Neurosurgical experiments and the concepts of Mishkin and Martinez support the idea that corticothalomo-hippocampal circuits are essential to the process of learning and memory ( 18, 19, 20 ). Taking into account their existence, the basic way of connections among neurons can be outlined by this fig. 4. Interneurons with manifest "long term potentiation" phenomenon ( symbolized on fig. 4 by "D") induce features of neural circuits, analogous to the described equi-me-rec units. Inter- neurons can change "the sign" and the amplification of "signals". Thus, sets of neurons interconnected in the way presented in fig. 4 (which is analogous to the equi-me-rec unit) can manifest high inclination for reverberating oscillatory flows of impulses.

The proposed data processing rules, occurring probably also in natural, neural circuits should facilitate the search form underlying intra cellular mechanisms realizing these processing phenomena, which will be described in terms of molecular, metabolic, enzyme and proteins changes. First of all, the molecular mechanism underlying the realization of so called D.O. Hebb rule, it means the change of "weights of synapses" during the learning process ( 21 ) should be proposed.

We would like to present here, for the discussion our hypothesis. Namely, it is possible that frequent perceptions, especially with 'attached' recalled mental images [ what is symbolized in our model by so called 'double energy ] - simply- change the mean , rather long lasting electrical potential gradient between the inside and the outside of the cell (10 ). This elevated, mean, long lasting electrical potential of any 'trained' neuron causes probably changes of 'weights' of these synapses, which were active.

Second most simple data processing feature, which should be explained in biochemical and bio-molecular terms it is the essence of the change of the set- point value.

Neural scientists will be interested probably into searching for the molecular, biochemical feature corresponding to the integrated quantity related to tuned properties of synapses of the neuron ( -w _n+1, -v _n+1). It would be a specific parameter of the trained ( 'learned' ) neuron important for its action.

It seems to us that the above considerations are important not only for neural scientists, but in the era of 'artificial intelligence', robotics and virtual reality also to some people who try to reproduce, in electronic circuits the phenomenon of the recalling of mental images.

CONCLUSIONS

1. The explanation of the recalling of the mental images requires the assumption of existence of the back - propagating, recurrent axons and "reconstructive" pathways .

2. It is possible to define a simple model of the neural circuit, characterized by reverberating activations, on the basis of feed- back loops composed with threshold logic units.

3. The oscillations in the hierarchical equilibrating, memorizing, recognizing and recalling unit can be initiated by the change of the value of the set- point signal given to the superior element of the unit.

4. The model indicates some data processing rules, which should be identified also in natural neural networks among molecular, metabolic intra cellular mechanisms.

5. The functional consistency of the model requires two different levels of the internal 'energy' ( ' arousal ' ) of the unit proper for simulation of: the 'perception' of the image and the 'recalling' of the image.

6. The double 'energy' is 'evoked' when the recalling of the image is 'attached' to the perception and probably in natural neural networks it is necessary for the change of properties of synapses according to the Hebb 's rule.

7. The mathematical analysis of the proposed elementary neural circuit indicates that a neuron utilizes for the data processing the signal ( quantity ) proportional to the memorized, summed, mean value of the 'weights of the synapses.

8. Neural scientists are challenged to search for the intra cellular, molecular, biochemical mechanism equivalent for the change of the set-point and for the integration of properties of synapses into a feature ( quantity ) appropriate for the control of the action of the neuron.

REFERENCES

1. Douglas RJ, Koch C, Mahowald M, Martin KA, Suarez HH : Recurrent excitation in neocortical circuts. Science, 1995, 269, 981- 985

2. Billock VA : Very short- term visual memory via reverberation: a role for the cortico-thalamic excitatoory circuit in temporal filling- in during blionks and saccades. Vision Res., 1997, 37, 949 - 953

3. Floresco SB, Braakama DN, Phillips AG : Talamic-cortical-striatal circuitry subserves working memory during delayed responding on a radial arm maze. J. Neurosci 1999, 19, 11061-11071

4. Kalivas PW, Churchill L, Romanides A.: Involvement of the pallidal- thalamo- corticalcircuit in adaptive behavior. Ann.N.Y.Acad.Sci., 1999, 877, 64 - 70

5. Kuroda M, Yokofujita J, Murakami K: An ultrastructural study of the neural circut between the prefrontal cortex and the mediodorsal nucleus of the thalamus. Prog.Neurobiol.,1998, 54, 417- 458

6. LaBerge D : Attention, awareness and the triangular circuit. Conscious. Cogn., 1997, 6, 149- 181

7. Shepard R.N.: Ecological constraints on internal representation: resonant kinematics of perceiving, imagining, thinking and dreaming. Psycholog. Rev., 1984, 91, 417-447.

8. Shepard RN : Toward a universal law of generalization for psychological science. Science, 1987, 23, 1317 - 1323

9. Pąchalska MM, Talar J, MacQueen BD: Disturbances of mental image processing in post-stroke patients with left and right hemisphere damage. Medical Science Monitor - in print

10. Brodziak A. The neurophysiology of the mental image. Medical Science Monitor - in print

11. Cannon W.: The wisdom of the body. London, Trubner and Co., 1932.

12. Wiener N.: Cybernetics or control and communication in the animal and the machine. New York, John Wiley and Sons, 1948.

13. Mc Culloch W.S., Pitts W.A.: A logical calculus of the ideas immanent in neurous activity. Bull. Math. Biophysics, 1943, 5, 115-133.

14. Nillson N.J: Learning machines. New York, Mc Graw Hill Inc., 1965.

15. Rumelhart DE., Hinion GE., Wiliams RJ: Learning representations by back-propagation errors. Nature, 1986, 323, 533-536.

16. Kohenen T: An introduction to neural computing. Neural Networks, 1988, 1, 3-6.

17. Grossberg S.: Nonlinear neural networks. Principles mechanisms, and architectures. Neural Networks, 1988, 1, 17-61.

18. Mishkin M.: A memory system in the monkey. Philos. Trans. Royal Soc. London (Biol.), 1982, 293B, 85-92.

19. Mishkin M, Appenzeller T: The anatomy of memory. Scientific American, 1987, 256, 61-71.

20. Martinez JL: Learning and Memory. San Diego- New York, Academic Press, 1986.

21. Hebb D.O.: The organization of the behavior. New York, John Wiley and Sons, 1949.

SUBSCRIPTIONS FOR FIGURES

Figure 1 The outline of the threshold logic unit

Figure 2 The outline of the feed - back loop

Figure 3 The outline of the equilibrating - memorizing - recognizing and recalling unit

( shortly: the equi - me - rec unit )\

Figure 4 The outline of a neutro - cyto - architectonic structure, analogous to the equi -me -rec unit.

The presented program, written in Logo language - will be reproduced soon in JavaScript (Java) language. It will be accesible here on this page

PPROP ".SYSTEM "BURY "TRUE TO GIVE'PATTERN IF :REPLY = [A] [PATTERN'CHAR] IF :REPLY = [B] [PATTERN'UN'CHAR] IF :REPLY = [C] [IF :IMPULS = 0 [MAKE "S' 2 MAKE "IMPULS 1] [MAKE "S' 0]] IF :REPLY = [D] [MAKE "S' 2] IF :REPLY = [E] [PATTERN] IF :REPLY = [F] [STOP] REMOVE2'TEXT WAIT 20 ACTION IF KEYP [SETCURSOR [22 0] REPEAT 35 [TYPE CHAR 32] SETCURSOR [17 0] PR [WE BEGIN THE RUN FOR THE SYSTEM AGAIN.] WAIT 50 SYMULATION STOP] GIVE'PATTERN END

TO PATTERN'CHAR MAKE "X1 1 MAKE "X2 1 MAKE "X3 1 MAKE "X5 1 MAKE "X6 1 MAKE "X7 1 MAKE "X9 1 MAKE "X10 1 MAKE "X11 1 PATTERN'FIG END

TO PATTERN'UN'CHAR MAKE "X1 0 MAKE "X2 0 MAKE "X3 1 MAKE "X5 1 MAKE "X6 0 MAKE "X7 0 MAKE "X9 0 MAKE "X10 0 MAKE "X11 0 PATTERN'FIG END

TO PATTERN MAKE "DATA :DATA + 1 IF :DATA > 1 [MAKE "X1 ITEM 1 :PATTERN MAKE "X2 ITEM 2 :PATTERN MAKE "X3 ITEM 3 :PATTERN MAKE "X5 ITEM 4 :PATTERN MAKE "X6 ITEM 5 :PATTERN MAKE "X7 ITEM 6 :PATTERN MAKE "X9 ITEM 7 :PATTERN MAKE "X10 ITEM 8 :PATTERN MAKE "X11 ITEM 9 :PATTERN PATTERN'FIG STOP] SETCURSOR [17 0] PR [GIVE THE CHOSEN PATTERN !] MAKE "X1 FIRST RL SETCURSOR [1 0] PR :X1 REMOVE'TEXT MAKE "X2 FIRST RL SETCURSOR [2 0] PR :X2 REMOVE'TEXT MAKE "X3 FIRST RL SETCURSOR [3 0] PR :X3 REMOVE'TEXT MAKE "X5 FIRST RL SETCURSOR [6 0] PR :X5 REMOVE'TEXT MAKE "X6 FIRST RL SETCURSOR [7 0] PR :X6 REMOVE'TEXT MAKE "X7 FIRST RL SETCURSOR [8 0] PR :X7 REMOVE'TEXT MAKE "X9 FIRST RL SETCURSOR [11 0] PR :X9 REMOVE'TEXT MAKE "X10 FIRST RL SETCURSOR [12 0] PR :X10 REMOVE'TEXT MAKE "X11 FIRST RL SETCURSOR [13 0] PR :X11 SETCURSOR [17 0] MAKE "PATTERN (SE :X1 :X2 :X3 :X5 :X6 :X7 :X9 :X10 :X11) END

TO REMOVE2'TEXT SETCURSOR [17 0] REPEAT 4 [REPEAT 35 [(TYPE CHAR 32)] PR []] SETCURSOR [17 0] END

TO ACTION CHANGE'FIG'3 NEURON'A NEURON'B NEURON'C REMOVE1'TEXT CHANGE'FIG'1 NEURON'2A CHANGE'FIG'2 END

TO PATTERN'FIG SETCURSOR [1 0] PR :X1 SETCURSOR [2 0] PR :X2 SETCURSOR [3 0] PR :X3 SETCURSOR [6 0] PR :X5 SETCURSOR [7 0] PR :X6 SETCURSOR [8 0] PR :X7 SETCURSOR [11 0] PR :X9 SETCURSOR [12 0] PR :X10 SETCURSOR [13 0] PR :X11 SETCURSOR [17 0] END

TO REMOVE'TEXT SETCURSOR [18 0] REPEAT 5 [(TYPE CHAR 32)] SETCURSOR [18 0] END

TO CHANGE'FIG'3 SETCURSOR [11 24] PR CHAR 32 SETTC [1 0] SETCURSOR [11 24] IF :S' = 2 [PR 1] [PR 0] SETTC [7 0] SETCURSOR [17 0] END

TO NEURON'A IF :S1 = 0 [MAKE "X4 0] IF :S1 = 1 [MAKE "X4 :X4 * :K] IF :S1 = 2 [MAKE "X4 1] MAKE "W1 0.9 MAKE "W2 0.9 MAKE "W3 0.2 MAKE "W4 1.6 MAKE "T1 1.1 MAKE "I :W1 * :X1 + :W2 * :X2 + :W3 * :X3 MAKE "R :W4 * :X4 MAKE "E :I + :R IF :E > :T1 [MAKE "Y1 1] [MAKE "Y1 0] IF :R > :T1 [MAKE "Y1 2] MAKE "X1 0 MAKE "X2 0 MAKE "X3 0 END

TO NEURON'B IF :S2 = 0 [MAKE "X8 0] IF :S2 = 1 [MAKE "X8 :X8 * :K] IF :S2 = 2 [MAKE "X8 1] MAKE "W5 0.9 MAKE "W6 0.9 MAKE "W7 0.2 MAKE "W8 1.6 MAKE "T2 1.1 MAKE "I :W5 * :X5 + :W6 * :X6 + :W7 * :X7 MAKE "R :W8 * :X8 MAKE "E :I + :R IF :E > :T2 [MAKE "Y2 1] [MAKE "Y2 0] IF :R > :T2 [MAKE "Y2 2] MAKE "X5 0 MAKE "X6 0 MAKE "X7 0 END

TO NEURON'C IF :S3 = 0 [MAKE "X12 0] IF :S3 = 1 [MAKE "X12 :X12 * :K] IF :S3 = 2 [MAKE "X12 1] MAKE "W9 0.9 MAKE "W10 0.9 MAKE "W11 0.2 MAKE "W12 1.6 MAKE "T3 1.1 MAKE "I :W9 * :X9 + :W10 * :X10 + :W11 * :X11 MAKE "R :W12 * :X12 MAKE "E :I + :R IF :E > :T3 [MAKE "Y3 1] [MAKE "Y3 0] IF :R > :T3 [MAKE "Y3 2] MAKE "X9 0 MAKE "X10 0 MAKE "X11 0 END

TO REMOVE1'TEXT SETCURSOR [1 0] PR CHAR 32 SETCURSOR [2 0] PR CHAR 32 SETCURSOR [3 0] PR CHAR 32 SETCURSOR [6 0] PR CHAR 32 SETCURSOR [7 0] PR CHAR 32 SETCURSOR [8 0] PR CHAR 32 SETCURSOR [11 0] PR CHAR 32 SETCURSOR [12 0] PR CHAR 32 SETCURSOR [13 0] PR CHAR 32 SETCURSOR [17 0] END

TO CHANGE'FIG'1 SETTC [1 0] SETCURSOR [6 27] PR 0 SETCURSOR [3 9] PR 0 SETCURSOR [8 9] PR 0 SETCURSOR [13 9] PR 0 SETTC [7 0] SETPC 2 IF OR :Y1 = 2 :Y1 = 1 [PU SETPOS [-80 102] PD SETPOS [-16 89] SETCURSOR [2 16] PR [1] WAIT 20 PU SETPOS [-80 102] PE SETPOS [-16 89]] [SETCURSOR [2 16] PR [0]] IF OR :Y2 = 2 :Y2 = 1 [PU SETPOS [-80 52] PD SETPOS [-16 74] SETCURSOR [4 16] PR [1] WAIT 20 PU SETPOS [-80 52] PE SETPOS [-16 74]] [SETCURSOR [4 16] PR [0]] IF OR :Y3 = 2 :Y3 = 1 [PU SETPOS [-80 2] PD SETPOS [-16 59] SETCURSOR [6 16] PR [1] WAIT 20 PU SETPOS [-80 2] PE SETPOS [-16 59]] [SETCURSOR [6 16] PR [0]] END

TO NEURON'2A IF :S' = 0 [MAKE "Y4 0] IF :S' = 1 [MAKE "Y4 :Y4 * :K] IF :S' = 2 [MAKE "Y4 1] MAKE "V1 0.9 MAKE "V2 0.9 MAKE "V3 0.2 MAKE "V4 1.6 MAKE "T 1.1 MAKE "I :V1 * :Y1 + :V2 * :Y2 + :V3 * :Y3 MAKE "R :V4 * :Y4 MAKE "E :I + :R IF :E > :T [MAKE "S 1] [MAKE "S 0] IF :R > :T [MAKE "S 2] MAKE "Y1 0 MAKE "Y2 0 MAKE "Y3 0 MAKE "S1 :S MAKE "S2 :S MAKE "S3 :S END

TO CHANGE'FIG'2 SETCURSOR [2 16] PR 0 SETCURSOR [4 16] PR 0 SETCURSOR [6 16] PR 0 SETCURSOR [11 24] PR CHAR 32 SETTC [1 0] SETCURSOR [11 24] PR 0 IF :S = 0 [SETCURSOR [3 26] PR 0 SETCURSOR [6 27] PR 0 SETCURSOR [3 9] PR 0 SETCURSOR [8 9] PR 0 SETCURSOR [13 9] PR 0 SETTC [7 0] STOP] PU SETPOS [40 77] SETH 90 PD FD 30 SETCURSOR [3 26] PR 1 SETPC 3 RESULT PU SETCURSOR [6 27] PR 1 PU SETPOS [40 77] SETH 90 PE FD 30 SETCURSOR [3 26] PR 0 SETPC 2 PU SETPOS [57 75] PD SETH 225 REPEAT 84 [RT 0.3 FD 2] SETCURSOR [13 9] PR 1 PU SETPOS [-11 21] PD SETPOS [-90 34] SETCURSOR [8 9] PR 1 PU SETPOS [-1 29] PD SETPOS [-90 81] SETCURSOR [3 9] PR 1 WAIT 20 SETCURSOR [6 27] PR 0 PU SETPOS [57 75] SETH 225 PE REPEAT 84 [RT 0.3 FD 2] PU SETPOS [-11 21] PE SETPOS [-90 34] PU SETPOS [-1 29] PE SETPOS [-90 81] SETTC [7 0] END

TO RESULT PU SETPOS [90 95] PD SETH 270 REPEAT 12 [LT 30 FD 8] WAIT 20 PU SETPOS [90 95] PE SETH 270 REPEAT 12 [LT 30 FD 8] END

TO HELP MAKE "HELP 0 SETCURSOR [22 0] PR [] SETTC [7 5] TYPE [F] SETTC [1 3] TYPE [orward..] SETTC [7 5] TYPE [N] SETTC [1 3] TYPE [ew run..] SETTC [7 5] TYPE [Q] SETTC [1 3] TYPE [-DOS..] SETTC [7 5] TYPE [S] SETTC [1 3] TYPE [top..] MAKE "REPLY1 RC SETTC [7 0] SETCURSOR [22 0] PR [] REPEAT 35 [TYPE CHAR 32] IF :REPLY1 = "N [TS CT SETCURSOR [5 0] PR [WE BEGIN THE RUN FOR THE SYSTEM AGAIN.] WAIT 100 SYMULATION] IF :REPLY1 = "Q [TS CT SETCURSOR [5 0] PR [WE RETURN TO DOS.] PR [TO START SYSTEM AGAIN :] PR [1 / LOGO] PR [2 / LOAD "STYMULATION] PR [3 / STYMULATION] WAIT 100 .DOS] IF :REPLY1 = "S [TS CT SETCURSOR [5 0] PR [THE FINISH OF THE SYSTEM] MAKE "HELP 1] END

TO FIGURE CLEAN TS CT HT LOADPIC "DISIGN SETTC [1 0] SETCURSOR [3 9] PR [0] SETCURSOR [8 9] PR [0] SETCURSOR [13 9] PR [0] SETTC [3 0] SETCURSOR [2 16] PR 0 SETCURSOR [4 16] PR [0] SETCURSOR [6 16] PR [0] SETCURSOR [3 26] PR [0] SETTC [1 0] SETCURSOR [6 27] PR [0] SETTC [1 0] SETCURSOR [11 24] PR [0] SETTC [7 0] SETPC 3 SETCURSOR [17 0] SETCURSOR [22 0] PR [TO INTERUPT STRICKE 'BLANK - BARR '] END

TO SYMULATION TS CT (SETWIDTH 80) MAKE "K 5 / 6 MAKE "IMPULS 0 MAKE "DATA 0 MAKE "S1 0 MAKE "S2 0 MAKE "S3 0 MAKE "S 0 MAKE "S' 0 MAKE "X1 0 MAKE "X2 0 MAKE "X3 0 MAKE "X4 0 MAKE "X5 0 MAKE "X6 0 MAKE "X7 0 MAKE "X8 0 MAKE "X9 0 MAKE "X10 0 MAKE "X11 0 MAKE "X12 0 MAKE "Y1 0 MAKE "Y2 0 MAKE "Y3 0 MAKE "Y4 0 PR [] PR [DETERMINE THE KIND OF EXPERIMENT. GIVE ONE OF FOLLOWING SYMBOLS :] PR [] PR [] (TYPE [A - HANDLING OF THE] CHAR 32 CHAR 32 [C H A R A K T E R I S T I C] CHAR 32 CHAR 32 [PATTERN ( IMAGE )]) PR [] (TYPE CHAR 32 CHAR 32 CHAR 32 CHAR 32 [FOR ANY CYCLE ( THE MODEL OF " P E R C E P T I O N "\)]) PR [] PR [] (TYPE [B - HAMDLING OF] CHAR 32 CHAR 32 [U N] CHAR 32 [C H A R A K T E R I C T I C] CHAR 32 CHAR 32 [PATTERN]) PR [] (TYPE CHAR 32 CHAR 32 CHAR 32 CHAR 32 [FOR ANY CYCLE ( THE MODEL OF UNKNOWN IMAGE )]) PR [] PR [] PR [C - ONE "ASSOCIATIVE" IMPULSE ( BIG SET'POINT VALUE FOR UPPER] (TYPE CHAR 32 CHAR 32 CHAR 32 CHAR 32 [SUBUNIT THE MODEL OF "MOMENTARY IMAGINATION" )]) PR [] PR [] PR [D - HANDLING OF "ASSOCIATIVE IMPULSES" FOR ANY CYCLE ( THE MODEL] (TYPE CHAR 32 CHAR 32 CHAR 32 CHAR 32 [OF A LONG IMAGINATION )]) PR [] PR [] PR [E - INPUT FROM YHE KEYBOARD OF THE PATTERN AND ITS HANDLING] (TYPE CHAR 32 CHAR 32 CHAR 32 CHAR 32 [FOR ONY CYCLE OF THE ACTION OF THE EQUI - ME - REC UMIT]) PR [] PR [] PR [F - FINISH] PR [] PR [] MAKE "REPLY RL SETWIDTH 40 FIGURE GIVE'PATTERN CT TS SETCURSOR [5 0] PR [WE RETURNED TO LOGO.] PR [] PR [TO START THE SYSTEM AGAIN WRITE :] PR [SYMULATION] END

The program in Logo language presents its action by means of the following figure.

Budowa i działanie mózgu
(Structure and the action of the brain)

Author of the website : Andrzej Brodziak
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