Visual illusions of the impossible figures.
How many bars do you see?

If you count the number of bars using the squares at the front, you'll find that there are eight total. But is it really that simple? Count the bars again, but this time use the end of the bars farthest away from you.

How is that possible?


According to the puzzle's creators, there are actually only six complete bars. You have to look very closely to see it. There are five complete bars clearly visible at the top. However, when you study the lines between the fifth and sixth bar, you'll find that they don't form a complete bar at all. They've just been added to trick you.


Blivet (Devil’s Fork)
Blivet appeared on the March 1965 cover of Mad magazine, where it was dubbed the “Three-Pronged Poiuyt”
(the last six letters on the top row of many Latin-script typewriter keyboards, right to left),
and has appeared numerous times since then.
Figure 2. Two-Pronged Trident

When an observer views a two-dimensional picture on paper, he often interprets it as a three-dimensional figure.
. . .

This insistence to view objects as three-dimensional objects can lead to interesting problems. For example, Figure 2 is upsetting to look at, since it appears to be a 3-D object, but the object seems to change its properties depending on how it is viewed. Covering the left side makes it appear as an object with two prongs. However, covering the right side makes it appear as an object with three prongs, not two. When the entire object is viewed at once, the object seems to switch between having two and three prongs. This impossibility confuses the mind.

If the figure was interpreted as a two-dimensional figure then it would be entirely possible and commonplace. It's simply three circles connected by a pattern of lines. If it were viewed in this way, then the mind would not be confused at all. "The fascination here is that the drawings are interpreted as representing objects, but the objects represented could not be constructed because the spatial constraints of the environment have been contravened.

These pictures work so well because they obey the pictorial rules in local regions but defy them globally. That is, the connections between regions that are presented in appropriate perspective are manipulated, and this creates the impossibility when an interpretation of the whole figure is attempted." (Wade, Nicholas. (1980). Visual Allusions: Pictures of Perception, pg. 16)


In other words, the figure uses pictorial rules to create the illusion of three dimensions, but then breaks some of these rules to make the object impossible to construct. Which rules are followed and which are broken determines the strength of impossible figures. A figure which doesn't follow any of the pictorial rules will look planar, and thus no object will be generated in the viewer's mind. Conversely, a figure which follows all of the pictorial rules will be easily represented in three dimensions in the viewer's mind. The interrelationships between the two opposite guidelines provides the illusion of an impossible picture.
Impossible Figures in Perceptual Psychology by Kevin Fink


Putting order in the impossible
Zenon Kulpa
Institute of Biocybernetics and Biomedical Engineering. 00-818 Warsaw Poland
[Published in: Perception, 1987, vol. 16, pp. 201-214]

The class of visual illusions called 'impossible figures' (illusory spatial interpretations of pictures) is analyzed in order to introduce an ordering into the great variety of such figures. Such an ordering facilitates reference, unifies terminology, and establishes a conceptual framework for further investigations of the subject, making easier the choice and systematic generation of various types of figures (for example, in systematic psychological experiments). First, the notion of 'impossible figure' is defined and certain other related classes of figures (so-called 'likely' and 'unlikely' figures) are distinguished. Second, the fundamental 'impossibility sources' are identified as elementary 'building blocks' of all impossible figures. Finally, two broad classes of impossible figures, multibars or ('impossible polygons') and striped figures, are briefly described.

Since the publication of the short paper by Penrose and Penrose (1958), so-called 'impossible figures' have increasingly attracted the attention of psychologists, computer scientists, and mathematicians. Psychologists study them as a new type of visual illusion (Penrose and Penrose 1958; Gregory 1970; Young and Deregowski 1981) providing information about mechanisms of visual perception, in particular the spatial interpretation of pictures (for example, Gregory 1970; Huffman 1971; Cowan and Pringle 1978; Young and Deregowski 1981; Kulpa 1983; Térouanne 1983; Thro 1983). For similar reasons they draw the attention of computer scientists who work in the field of computer vision and try to create computer models of human perceptive abilities (Huffman 1971; Sugihara 1982a, 1982b; Kulpa 1983). Finally, for mathematicians they represent new types of abstract structures to be formally studied (Huffman 1971; Cowan 1977; Térouanne 1980, 1983). It should also be mentioned that these effects are of increasing interest to the theory and practice of visual arts and graphic design (Ernst 1976, 1985, 1986; Yturralde 1978; Reutersvärd and Kulpa 1984), and that they are also discussed in the contexts of logic and the philosophy of language (Cresswell 1983).

The presentation of just a few examples of the most well-known impossible figures (figure 3) is sufficient to demonstrate the considerable diversity of types that exists. Many more examples could be given, and it is therefore important to find (or impose upon) these figures some ordering principles and classification schemes.

Figure 3. Four examples of impossible figures: (a) Penrose's tribar; (b) devil's fork; (c) Thiéry's figure; (d) impossible ring

In this paper I propose and briefly discuss several basic ordering schemes. The presentation starts, in section 2, with the definition of an impossible figure (Kulpa 1983) and a general classification that relates impossible figures to possible figures, and also to special classes of figures called 'likely' and 'unlikely' (Huffman 1971; Kulpa 1983). The problem of various degrees of impossibility is also introduced. In section 3 the fundamental 'impossibility sources' are identified (Cowan and Pringle 1978; Kulpa 1983; Thro 1983) as elementary 'building blocks' of all impossible figures. Finally, in sections 4 and 5, two broad classes of impossible figures, namely multibars (Cowan 1977; Draper 1978; Térouanne 1980; Kulpa 1981) and striped figures (Robinson and Wilson 1973), are briefly described.

The classification schemes described in this paper are based partially on my own investigations (Kulpa 1981, 1983), and partially on the work of others, especially Huffman (1971) and Cowan (1977). Certain other classification schemes, unrelated, in principle, to those I discuss below, have also been proposed. Guiraud and Lison (1976) tried to systematize, from the graphic designer's point of view, the multitude of ambiguous figures based on the principle behind Thiéry's figure (Thiéry 1895; see figure 3c). On the other hand, Sugihara (1982a, 1982b) suggested the general classification of so-called "labelable figures" (which include many possible and impossible figures) according to features significant for certain types of computer algorithms of automatic scene analysis.

Striped figures
Various kinds of impossible figures (Robinson and Wilson 1973; see figure 4a) can be interpreted as a sequence of stripes, that is, elongated areas separated by straight parallel edges, according to the general scheme of figure 17b, where the symbols I1, I2, ..., In and J1, J2, .... Jn denote appropriate (spatial) interpretations of the stripes as suggested by pictorial contexts at their respective endings. When interpretations I and J of a stripe are different a contradiction occurs, and perhaps eventually produces an impossible figure.

Figure 4. (a) Four examples of striped figures, (b) general scheme of a striped figure.

How many Shelves are there?
Are there three or four arms?

• Wade, Nicholas. (1980). Visual Allusions: Pictures of Perception. Hove, UK: Lawrence Erlbaum Associates Ltd.
• Cowan T M, 1977 "Organizing the properties of impossible figures" Perception 6 41-56
• Draper S W, 1978 "The Penrose Triangle and a Family of Related Figures" Perception 7 283-296
• Ernst B, 1976 The Magic Mirror of M.C. Escher (New York: Ballantine Books)
• Gillam B, 1979 "Even a possible figure can look impossible!" Perception 8 229-232
• Kulpa Z, 1983 "Are impossible figures possible?" Signal Processing 5 201-220
• Thro E B, 1983 "Distingushing two classes of impossible objects" Perception 12 733-751
• Young A W, Deregowski J B, 1981 "Learning to see impossible" Perception 10 91-105

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