III. Examples of gestalt laws

1. XA-laws 

Attention is familiar to us from our everyday experience (Part 5). In the realm of visual perception, directing and withdrawing the attention takes the form of directing or withdrawing one's gaze. We are capable, however, also of looking straight ahead, and simultaneously directing our attention to a peripherally perceived event. Let us now express several everyday experiences in the form of gestalt laws. Since attention is not confined to the realm of visual perception, we may choose examples also from other realms of experience. We know that the more we direct our attention toward a certain object (ic), the less attentive we are toward everything else (o) that takes place around us (Aic ao). That, which suddenly appears attracts my attention (dtic Aic); the longer it is to be seen, the less it captures my attention (Dti aic). We may then logically conclude: if dtic Aic and Aic ao, then dtic ao as well; this corresponds to our experience, for when something suddenly happens, we withdraw our attention from everything else, we look up from our book, we interrupt our conversation, and so forth. In the presence of a loud conversation I am distracted from reading; in order to be able to "concentrate" on reading I must intentionally "tune out" what I hear. In this example, when I intentionally and "voluntarily" withdraw my attention from the outfield (o), it is then "automatically" and "involuntarily" directed all the more to my reading. Voluntary attention is the independent variable here; its term is on the left, and the AA-law then has the form ao Aic (or: aic Ao, depending on how one assigns the indices i and o to what is heard and what is read). Incidentally: I admittedly do not know if it is possible to voluntarily withdraw attention; possibly this may be achieved only by focusing the attention to a greater degree on something else, as was the case of "concentrative withdrawal of attention" in Part 6. Everybody knows that objects attract our attention more than their surroundings. Thus, a figure attracts our attention more than its outfield, corresponding to the gestalt law Flic Aic. 

2. Xdt-laws 

The "inverse law" of dtic Aic is Aic dtic. This law, too, is well-known from everyday experience, as the factor Dt ("time difference") is likewise not a specifically visual factor: it is according to this law that "time flies when you're having fun" (because one's attention is focused on something particular when "having fun"). Conversely, when we have to listen to a boring speech (ic), it seems to take forever, and we experience the speech as lengthy: aic Dtic. The class of Xdt-laws consists of those laws that influence the experience of duration and temporal interval; latency and "time-order error" belong to this phenomena group. When I first began to interpret findings dealing with change in latency, i.e. the time span between stimulation and experience, I assumed that this time had to be the "time-outfield" (Lt-,Ft-), because it does in fact lie outside both the beginning and the end (Ft+) of "duration" (Lt+). But I failed to come to the interpretation expected. Only when I proceeded from the contrary assumption that the latency was located, just as the subsequently experienced duration was, within the time infield (Lt-,Ft+), were all symbolic notations reducible to the standard notation. A good example of how one can stumble over surprises in the process of interpretation. Of course, one must give some thought as to how such an unexpected result can be integrated into the system of gestalt laws. This may be achieved if we recall that each phenomenon, each gestalt quality, is merely an "epi-phenomenon" of its underlying gestalt factor; the actual location of an event is not the phenomenal sphere, but the functional sphere. The latency is thus simply the quantum of temporal delay between the onset of the functional activation process and the subsequent onset of the phenomenon, i.e. the actualization. (Because the physical functions, and in particular the excitation of the lowest-level neurons, are located beneath the system of gestalt functions, it is possible to view the latency as the time necessary for the transmission of the neural signal from the  location of stimulation to the location of sensation.) 

It follows that, according to the law Aic dtic, directing the attention toward a stimulus reduces its latency. In this way, it can happen that a light stimulus occurring at an objectively later time, but which is being viewed more directly, can be detected before a light stimulus originating at an objectively earlier time. The latency of the latter stimulus is larger because less attention is directed toward it. What follows is an example of the so-called "time-order error".

The law dl dt leads to the phenomenon known as the "KAPPA effect" (Cohen, Hansel & Sylvester 1953): when three light stimuli are produced at equal temporal but unequal spatial intervals, those stimuli separated by smaller spatial intervals are perceived as occurring at smaller temporal intervals than those stimuli whose spatial separation is larger.


Figure 8-2. Spatial and temporal relationships in the KAPPA-effect

In Fig. 8-2A, the objective spatial ico-relationships of the stimuli p,q, and r are shown: they are planar figures ic of equal size. They differ only in respect to the size of their planar outfield o, and especially in respect to the partial outfields between the figures: the outfield between q and r is smaller than the outfield between p and q. Fig. 8-2B shows the objective temporal relationships: the three stimuli are all produced for the same length of time, and the intervening "time outfields" are likewise of identical length. The time figure (according to Part 7) consists of the time infield i, i.e. the duration of time for which the figure exists, and the temporal borders c (the "beginning-border" c1 and the "ending-border" c2) that "enclose" the "time infield". The KAPPA phenomenon, in which the temporal relationships are as shown in Fig.C, may be described verbally as follows:

The smaller the planar outfield o (Fig.A),
the smaller the temporal outfield o (Fig.C).

A more exact description is even better:

The smaller the location differences (Dl) of the ico-systems, as measured across their outfield o,
the smaller the time differences (Dt) of the ico-systems, as measured across their outfield o. 

Symbolic notation: dlo dto. By performing two transformation operations, as permitted by the transformation rules, we obtain one of the four standard notations such as Dlo Dto, or dlic dtic. We have thus traced the KAPPA phenomenon back to one of the 324 predicted gestalt laws. 

Elder and Zucker (1993) investigated the search task response time for the figure  discrimination of different degrees of closedness. They found that closing the figures dramatically enhances the discriminability. We can purely formalistically write the symbolic expression Flic dtic, in which the discrimination time is treated exactly like the latency, that is as "belonging" to the figure. 

In another series of experiments, the same authors compared closed figures that were, on one hand, formed by solid lines and, on the other, by broken lines. The sets of figures thus possessed different degrees of linearity (Ll+). The fewer gaps a contour exhibits, the more the gestalt stimulus for the actualization of the gestalt function Ll+ is present, as reflection upon the gestalt stimulus definition for Ll+ (and admittedly a corresponding expansion of this definition) should make clear (see also Part 2). The more a figure contour is an Ll contour, the more it borders a field as infield off from the remaining field as outfield according to the law Llc Flic. When Llc Flic and Flic dtic, then also Llc dtic. This law describes the dependence of time for the discrimination of a figure from the degree of continuity (Ll+) of the figure contour.  

3. Xdl-laws 

The "inverse" phenomenon of the KAPPA effect is the TAU phenomenon. This phenomenon was investigated in greater detail by Helson (Helson 1930; Helson & King 1931) in the context of cutaneous modality. The authors were able to show that when cutaneous stimuli are presented to subjects at equal spatial but unequal temporal intervals, those stimuli separated by smaller temporal intervals are perceived as lying closer to one another (dto dlo or Dto Dlo). In the context of visual perception, this phenomenon was reported by Benussi (1913).  

Several examples of the specific gestalt law dl dl exist, which are well-known as "geometric optical illusions". Among these are the Moon illusion as well as the Delboef and the Ebbinghaus illusion. The "specific gestalt law" of a gestalt factor designates that particular gestalt law according to which a gestalt factor interacts "with itself", as it were. In the case of the factor Fl, for example, the law Fl Fl is the "specific law of closedness". In the case of the factor Dl, it is the law dl dl. This is the "specific law of location difference", since Dl symbolizes the separation of two locations in the frontal parallel plane and thus the separation of two stimulus points on the retina. All gestalt laws, in which two different factor symbols are combined, are "unspecific gestalt laws". Both kinds of laws receive the same formal treatment. The formulation of any gestalt law comprises also the formulation of the relevant polarity laws. 

a) The Moon illusion 

One can experience the "Moon illusion" for oneself on nights when the moon is out; at the zenith, when high in the sky, the moon clearly appears to be smaller than when near the horizon. The Moon illusion has already been discussed at great length in literature. From the point of view of the interaction theory, the concrete figure/outfield relationship must be elucidated: the bright and clearly delineated moon has the effect of a strong "figure", the dark homogeneous sky that of the outfield of this figure. Upon examining all 18 interaction factors in greater detail, one finds only a single factor in respect to which an unequivocal difference exists between the moon at the zenith and the moon at the horizon. To begin with, we can automatically exclude all factors with depth (d) and time (t) aspects, as already mentioned. Furthermore, the sharpness (Gml+) of the moon edge, the homogeneity (Gml-) of the fields, and the brightness difference (Dm+) between infield and outfield all fail to exhibitit any substantial difference in the two cases. In addition, there is no difference in either the linearity (Ll+) or the closedness (Fl+) of the contour. There is, however, one notable difference: when the moon is at the zenith, it is surrounded by a very large outfield, but the outfield of the horizon-moon is only half as large, due to its being bounded on one side by the silhouette of the landscape, the "horizon". 

When we formulate our observations of the moon, in the transition from the zenith-moon to the horizon-moon in terms of the interaction theory, we have: "The smaller the outfield is (objectively, as a sensory stimulus), the larger the figure appears". Symbolically, this can be expressed: dlo Dlic. After performing two transformation operations, as allowed by the transformation rules, we obtain the logically identical espression Dlo dlic, a standard notation, that denotes the same law in the case of the moon, in the transition from the horizon-moon to the zenith-moon. The Moon illusion can thus be traced to the specific gestalt law "dl dl", of the gestalt factor Dl. This may not be the whole story about the Moon illusion, but it is the crux of the matter. The possibility that other factors affect the apparent size of the moon is not to be excluded; theoretically, there are at least 18 factors capable of influencing the apparent size of the moon.  

So much for the theory. What about the empirical findings? Rock and Kaufman (1962) performed experiments in which subjects were instructed to judge the size of the moon in two different cases: on one hand, when the outfield of the moon was bounded by a silhouette of New York, and on the other, when it was unbounded, as the moon would appear when high in the sky. After having determined that the influence of other possible factors was negligible (see also Kaufman and Rock 1962), they arrived at the following conclusion: "It seems clear, then, that it is the presence of terrain in one case and the absence of terrain in the other that is the major factor in the Moon illusion." (p.1025). Not only in field experiments, but also in drawings, as well, the presence of terrain in the case of the moon at the horizon proved to be the deciding factor in the Moon illusion (Coren and Aks 1990).  

b) The Delboef illusion 

The well-known "Delboef illusion" (Delboef 1893), too, follows the dldl-law. Figs. 8-3A, B, and C all depict two concentric circles. Although the inner circles are all same size, the inner circle in B appears to be larger than in A, and likewise, the inner circle in C appears to be larger than in B. This must be due to the different sizes of the outer circles, as other differences are not to be found. In interpreting this observation, we shall proceed according to the method cited above: 

Figure 8-3. Delboef illusion 

1. In the transition from A to B to C, the objective size of the stimulus changes as well as the experienced size. We are thus dealing with the effects of that gestalt law whose general notation is "dl dl". 

2. In the transition from A to B to C, the experienced size (Dl) of the dependent variable increases whenever the objective size (Dl) of the independent variable is decreased. Applying the notational rules regarding the capitalization (or lack of it) of symbolic expressions we can thus write "dl Dl".  

3. The ico-relationships must be analysed, i.e. the gestalt locations at which the size changes take place, are yet to be determined. A simple interpretation would be to view the inner circle (Fig.D) as the contour c of a figure ic, so that the field within this contour is the infield i of the figure. This figure must possess an outfield o. This is the field that encloses the figure ic. 

At this point an additional note is necessary: "circles" may exist in geometry, but they do not exist in our visual system, at least not as independent perceptual entities. What does exist in this context are borderlines and fields, as also their figure/outfield unions. Among these may be  counted, as  examples,  the  figure  "formless  disk" (Part 6), and the figure "circlelike ring". When dealing with Delboef patterns, we are dealing with just these types of figures, so that we are required to speak of "disks" instead of "circles". For the sake of simplicity, however, we shall continue to speak of circles, when this does not affect the line of argument. 

4. We are now ready to verbally formulate the dldl-law at work here: "The smaller the outfield, the larger the infield". The corresponding symbolic expression of this gestalt law is: dlo Dlic. 

5. By performing a validity check we ascertain that, although neither of the two phrases in the above notation are to be found in the double basis row, they can nevertheless be converted into a standard notation by performing an even number of transformation operations. Doing so, a standard notation of a valid gestalt law is produced, for example Dlo dlic. (For every gestalt law there are eight valid notations, four of which are standard notations, as shown in Table 8-1.) 

c) The Ebbinghaus illusion 

In both Figs. 8-4A and 8-4B we have circles of equal size, in the Ebbinghaus patterns, surrounded by six other circles. These surrounding circles are smaller in A than they are in B. In A, the inner circle appears to be larger than in B. If we take the inner circle to be figure ic then all the outer circles are located in its outfield o. Now the other circles are likewise figures, in respect to which the inner circle is located in their common outfield. This is another possibility of interpreting the stimulus pattern. We must choose one of these alternative possibilities of establishing the ico-relationships. If we choose the second alternative, so that the outer circles are figures with the inner circle located in the common outfield (8-4C), then we find that the gestalt law variation Dlic dlo (read from A to B) holds: "The larger the figures ic, the smaller the outfield o, and consequently, the smaller the figure(s) located within this outfield, i.e. here: the inner circle." Or (read from B to A): "The smaller ic, the larger o" (dlic Dlo). Instead of using the size of the (two-dimensional) field, one can use also the size of the (one-dimensional) location difference: "The smaller the location differences of contours (lines) are, as measured across the infield, the larger the location differences appear, as measured (or estimated) across the outfield."

Figure 8-4. Ebbinghaus illusion 

The Ebbinghaus illusion bears a certain similarity to the Delboef illusion. Not only do the same gestalt laws hold for both, as we have just demonstrated; there are structural similarities as well. In the Delboef  illusion, a linear ring surrounds the standard circle; in the Ebbinghaus illusion, a ring of circles surrounds the standard circle. This similarity led Girgus, Coren and Agdern (1972) to question whether varying the separation between the inner circle and the ring of circles would have an effect on the judgment of the size of the inner circle in the Ebbinghaus illusion. It did, and in fact, in the same way as produced by varying the size of the outer circle in the Delboef illusion. This effect was reported also by Massaro and Anderson (1971). To elucidate in the terminology of the ETVG: if we take the inner circle to be ic, then the outer circles are located in the outfield o of ic. In addition, these six circles can be compared with the outer circle of Fig. 8-3D. If the ring of outer circles is moved away from the inner circle, i.e. is expanded, then the immediate outfield between the i-border c and the ring of outer circles bordering o is enlarged as well. Consequently, the inner circle ic appears to be smaller. 

Thus, we have two possibilities for interpreting the Ebbinghaus illusion: on one hand, the entire perceptual field enclosing the inner circle is viewed as the outfield, so that the outer circles belong to the outfield. On the other, we can view the field between the inner and outer circles as the outfield, so that the outer circles do not actually belong to the outfield but instead form its border. Which interpretation is correct? The answer is simple: the two interpretations are not mutually exclusive. And this not merely in a logical sense but also as far as the structure and function of the visual system are concerned, for we perceive at various hierarchy levels and by means of a large number of perceptual factors. The effects of these factors do not preclude one another, but rather integrate with one another, and this in respect to different locations, i.e. "gestalt locations". In the experience of the individual, it happens often that antagonistic factor effects mutually exclude each other, leading to the phenomena of ambiguous figures. 

By the way, I would suggest using the "abbreviated" Ebbinghaus illusion as depicted in Fig. 8-4D for lecture demonstration. 

Hildebrandt and Kleinknecht (1975) introduced small gaps of equal size to the inner circle of the Ebbinghaus pattern. They found that the gap in the B-variation, the variation with the larger outer circles, was noticed significantly less often than in the A-variation. The "compression" of the center circle due to the presence of the larger figures had affected also the apparent size of the gap, so that the gap in the more compressed inner circle sank below the location difference threshold more often (thus making it imperceptible) than in the less compressed inner circle (in Fig.8-4A).   

Figure 8-5. Demonstration of the gestalt law Fl dl 

The early psychophysicists used to believe that a certain physiologically determined "absolute" difference threshold of constant magnitude exists. In their investigations, however, they always obtained different results, depending on the targets and experimental procedures in each specific case. It is now generally accepted that such absolute, quantitatively determinable thresholds do not exist, but it is still not known which factors the threshold is in fact dependent upon. The interaction theory might prove helpful in accounting for varying "absolute" (and "relative") thresholds.  

Fig. 8-5 demonstrates the law Fl dl: the more a figure is closed (A in opposite to B) the smaller appears a spatial interval of certain length, within the figure, or figure contour. The same gestalt law operates in the experiments of Coren and Girgus (1980). The authors showed that an spatial interval within a group-figure (here: within the contour of a dotted square) appears smaller than an interval of equal length, in the figure's outfield (Flic dlic).  

In the same work Coren and Girgus reported an experiment in which the subjects were exposed to parallel rows of black and white figures. The subjects interpreted the black figures as forming one unit, and the white figures another - in accordance with both the "law of similarity" of the early Gestaltists and the gestalt law "dmic Flic" of the ETVG. The subjects were then asked to judge the spatial interval (location difference) between a black row and a white row and between two white rows. Although all intervals were objectively equal, the interval between the same-colored rows was judged smaller than that between the different-colored rows. One can simply use the law dmic dlic, from which we obtain, "the more two stimuli have the same color the closer together they appear to be located." Based on the intervals between the same-colored objects, we would, in respect to the larger phenomenal intervals between the different-colored objects, better use the corresponding law Dmio Dlo. 

4. XFl-laws 

The XFl-class of laws includes those laws that influence the particular properties of the gestalt factor Fl, and thus the closedness/openness of the borderline, the enclosing/enclosed relationship of fields, and, consequently, the intensity of the "figure/outfield" experience. These are also the laws that actually constitute a figure/outfield system; they are laws for the formation of figures. Furthermore, they are grouping laws, since a group of figures is a figure of a higher-order (Part 6). It is some of these laws that the early Gestaltists termed "gestalt laws", without, however, having ever grasped them in their entirety, without having recognized their interrelationships, and without having provided them with a form with which they could have served further theoretical investigation of visual perception. Over a period of research lasting several decades, which was, admittedly, experimen- tally very fruitful, the Gestaltists nevertheless hardly refined their gestalt laws. What one reads to this day about these laws is essentially that proposed by Max Wertheimer (1923), seventy-seven years ago. In the last few years, experimental research has increasingly taken up the "gestalt" predictions of the Gestaltists, but usually in order to prove them incorrect.  

New results are rare. Palmer (1992), however, proposed a previously undescribed grouping law: figures that share a common outfield are grouped together. In Palmer's designs the outfield is in turn bounded. According to the ETVG, the bounded outfield itself thus forms a figure, a superordinate figure, a second-order figure  in respect to the enclosed first-order figures (Part 6). Everything inside a field that is contour-enclosed (Fl) is part of this field, which is an infield, und thus the things belong to the figure, consisting of this infield and the infield-enclosing contour. A number of figures in an, in principle, unbounded outfield share this common outfield; there is nothing peculiar about it. The new observation of Palmer is that part A of the figures that is bordered off against the other part B is grouped together. With the help of the closed border round part A a new outfield for the A-figures has not been created, but it has been a new (a second-order) figure developed, whose infield the A-figures now belong to. I propose to relate the observed grouping of the A-figures to the new (second-order) figure and not to the (first-order) outfield. The gestalt law operating here is Flic Flic: the more a contour (c) encloses (Fl) a field (i), the more a figure (Flic) develops, and all things A laying on the infield are part of this figure; all other things B do not belong to this figure, they lay outside in the figure's outfield. Now, A-things and B-things are as different as are figure and outfield. 

One of the most well-known grouping laws is the "law of proximity", as was first shown by Schumann (1900). As seen in Fig.8-6A, two lines that are close to each other are more often grouped together than two lines lying farther apart. The correspond- ing ETVG law is: dlic Flic. Wertheimer (1923), who introduced this among other laws into Gestalt psychology, expressed himself more cautiously: he spoke of a "factor of proximity" and not of a "law of proximity". 


Figure 8-6. Demonstration of the "law of proximity" (dl Fl) 

Example 8-6A, however, is not the most auspicious one, as these lines are not perceived as "belonging together", as forming a group, a superfigure, on account of their proximity alone. Another grouping factor likewise named by Wertheimer, the "factor of closedness", too, plays a role, because those lines that are closer together enclose the intermediate field to a greater degree than the lines that are farther apart. In this respect, the law Flic Flic works in the same direction as the law dlic Flic. In contrast, the factor "closedness" does not play the same role in the case of Fig. B; here, the law of poximity is envinced in a purer form. 

Fig. 8-7 shows two examples of the grouping of square figures on the basis of smaller location differences between the figures in each respective case. In A, one might experience the pattern as "two single squares three times"; it is already clear in this formulation that the perceiver has imposed a grouping on the pattern; the two squares in close proximity are seen as a unit that appears "three times". At the same time, this unit is experienced as consisting of two single objects, or components. Those squares that are somewhat farther apart from each other are not experienced as belonging together, or at least not to the same degree as in the case of those squares that are close to each other. If one says that one sees "three pairs of squares" then the "unit consisting of two components" has been perceived as even more of a unit than before, in the preceding case; thus the name "pair".


Figure 8-7. How can one perceive the six squares?    

 In 8-7B, there are likewise six squares; they differ from A only in that they are all spaced at equal intervals. Nobody would claim that three pairs of squares are given in this example; there is no reason to subdivide these six squares any further. Here one tends to use a different expression, sometimes along the lines of "here is a row of squares". One is unlikely to say: "here are six squares", because six figures are much more difficult to grasp as a particular number than two or three figures are (see the quantity factor in Part 5). In order to say the latter, one would first have to count the six squares, which is a mental process and not a perceptive one. The single figures have already lost a certain degree of figuredness and are grasped as the components of a "row", which in turn represents a superordinate figure in respect to the single figures. If one says that Fig. 8-7B is a "line of squares", then this decrease in the figuredness of the individual figures, has been even more strongly experienced. Whereas the word "row" suggests that an element of discreteness has been experienced, caused by the individual squares, "line" suggests more of a continuum.  The gestalt stimulus for the gestalt function "Ll+" exists in both cases, but function Ll+ is activated in the case where the "line of squares" is experienced stronger than in the case where "row of squares" is experienced.


Figure 8-8. Which logical possibilities exist to perceive the four dots of A?

 In Fig. 8-8A, one sees four dot figures. One sees, voluntarily or not, also their "square" configuration, where a "square" is the superfigure (a second-order figure) composed of four dots, repre- senting first-order figures, and perhaps someone claims to see a "dotted square". Such experiences are determined by the constraints of the figure formation law dlic Flic, which is active also in Example 8-7. In Fig. 8-8, those figures ("dots") that are located closer to each other are experienced as belonging together (and thus forming a superordinate figure), but those that are farther apart are not experienced as belonging  together. It is for this reason that Pattern 8-8A is spontaneously experienced as a square, as shown in 8-8B, and not a cross as in C, where the diagonal intervals are larger than those forming the sides of the square. The four-dot pattern is also not spontaneously experienced as shown in 8-8D, E, and F, otherwise some dots of equal spatial intervals would be experienced as belonging together, and some not. In addition, an even longer interval in F would be connected, but shorter ones remained unconnected. (Of course, one can "voluntarily" perceive all the "unnatural" Figures 8-8 C to F.)  

The early Gestaltists were often more interested in demonstrations than in quantitative investigation, and so it is no surprise that there seems never to have been any systematic investigation of their "factor of closedness", according to which, for example, lines tend to join together to form the contours of two-dimensional figures. Bobbit (1942) recognized "that progressive changes in the degree of completeness of a figure result in a rather sudden change in the way the presentation is organized" (p.289). He thus recognized that the factor of closedness possesses a threshold; this threshold is, according to the ETVG, the "actualization threshold" of the gestalt factor Fl. Bobbit also found that "there are obviously many factors influence the closure threshold" (p.286). Reformulating these factors of influence into the ETVG terminology would, no doubt, prove interesting.  Gillam (1975) used  depth  ambiguity  to  investigate  closure. She used stimulus patterns consisting of a field and an enclosing  line that was  not completely closed but contained a "gap". The author found that "closure is an inverse monotonic function of gap size" (p. 522). If one substitutes "degree of non-closedness of the contour" for "gap size", then the law flic flic may be applied. In this case, there can be no objections if we drop the index "i" from the left-hand term in order to designate this variable with greater efficency (since closedness of contour was spoken of, not of infield). We can thus write "flc flic". A certain latitude exists in the choice of indices; one must, however, always be aware of what is meant. 

Fig. 8-9A shows a well-known pattern: a circle that has been divided into sectors of unequal size. Fig. 8-9B illustrates the "gestalt location relationships": we indicate (arbitrarily, but expediently) those sector fields forming the spontaneously appearing figure, perceived as a cross with i, the contours enclosing these fields with c, and those fields outside of the infield that enclose the figure ic, with o. When one looks on the center of  figure A, one often spontaneously sees a cross-like figure formed by the smaller sectors, i.e. the sectors whose contours lie in greater proximity - according to the law dlic Flic. We can formulate the relationship governing the formation of this figure also by proceeding from the field o: the larger the location difference between the contours c as measured across the enclosing outfield o, the more the contours c together with the enclosed field i are experienced as a "figure": Dlo Flic. After viewing the pattern A for some time, the figure suddenly turns into the cross formed by the wider sectors - according to the law Dtic Flo (or Dtic Floc). One can account for such a switch with a "saturation effect" or a "fatigue effect". But such terms make sense only as long as one has access to some sort of comprehensive theory, in which "saturation" and "fatigue" are relevant concepts; otherwise we have nothing but an ad hoc explanation that fails to tell us anything new. The ETVG makes no mention of "saturation" or "fatigue"; the 324 gestalt laws are formed by other concepts.

If one focuses one's gaze directly to one of the wider sectors, the wider cross usually appears more often spontaneously: the law Ao Flo works in opposition to the law Dlo Flic, or dlic flo.

 Figure 8-9. Sector illusion  

The disk in Fig. 8-9C has been divided into sectors of equal size. This pattern can be experienced, with almost equal likelihood, in two different ways. We  have  already  encountered  two  such   stimulus patterns: the "vase/faces" pattern (Fig. 2-10) and the "Necker cube" (Fig.2-11). According to the ETVG, the "reversal" from one interpretation to the other happens because the stimulus pattern contains two sets of gestalt stimuli that actualize the gestalt factor Fl. It is likely in this case, that the actualization threshold of both sets of gestalt factors are equal, so that it is a matter of chance which interpretation appears first. In this case of Fig. 8-9C, a labelling different for the fields to that in the case of B is more appropriate. Each of the two alternately appearing crosses is perceived as a figure, with one termed Figure 1 and the other Figure 2, as shown in Fig. 8-9D. Based on the coincidental appearance of Figure 1, the "switch law" is: Dt1 Fl2, or Dtic Flo. Through allowed transformation the standard notation dtic flo is developed.   

This gestalt law can be reached also in two or three steps, for example:

In this way the relationship Dt1 Fl2 is produced. There is nothing to be objected to in such a procedure; indeed, it is often helpful in understanding a phenomenon to proceed in several steps. The orientation factors V and H, too, can create certain configurations, as shown in Fig. 8-9E. Furthermore, a threeness of figures may occur. 

According to Koffka (1935, p.153), the "Law of good continuation" of the early Gestaltists can be manifested in both that

Koffka elucidated the law of good continuation with the aid of concrete examples, cited above, so that it is quite clear what is meant by them. It is somewhat more difficult, however, to give this law a general verbal form. Occasionally authors stress the continuation of the identical or nearly identical orientation: at an intersection, the less the orientation of continuation of a line deviates from its previous orientation, the more it is a "good" continuation.  Fig. 8-10A shows an example of this "law". One sees a straight line intersecting a curved line (B) or a curved line intersecting a straight line (C) rather than the configurations shown in D or E.  

Figure 8-10. One stimulus (A), and four possible percepts  (B to E)

According  to the ETVG, however, "good continuation" has nothing to do with the experienced orientation. Also the explanation, that curves follow their "natural way", does not lead us anywhere. According to the ETVG, the "good continuation" is an immediate effect of the fourth-level gestalt factor "line" in its positive function (Ll+) (see the gestalt stimulus definition for Ll+ in Part 2) and not an effect of the ninth-level straightness factor S. At the intersection of lines 1-2 and 3-4 in the stimulus of 8-10A, the sum of Dls is maximum in the case of a "straight" continuation from 1 to 2, and nearly maximum in the case of 3 to 4. The gestalt law in operation here is to be assumed Llc Flic, when the "line" 1 to 2 is perceived as an "elongated figure" (Fl,E). The quantity factor, too, is in operation, as the perception of a single (Q1) line figure requires less actualization energy than the perception of two (Q2) line figures adjoining each other at the intersection. Figs 8-10D and E show further possibilities of experiencing pattern A. Here, not line figures (at the E-level) are seen, but field figures (at the Fl-level), in which the "lines" form the contours of a more or less closed figure. This closing of the field occurs in accordance to the gestalt law dl Fl, but interpretations B and C alternate, as B and C interpretations in turn alternate predominantly with E.  Once again, we are dealing with "ambiguous figures". It is not possible to experience the "line" and "field" phenomena simultaneously, as they are mutually exclusive, which has already been explained in Part 2.  

Excerpt from L. Kleine-Horst: Empiristic theory of visual gestalt perception. Hierarchy and interactions of visual functions. (ETVG), Part 8, III.

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