Illusions Involving Oscillation of Attention

There are curious geometrical illusions that are not concerned with false assessments of sizes or angles.  Instead, they arise from a difficulty in distinguishing what might be termed positive and negative interpretations of an image pattern. 

Fig. 71 and 72 show photographs of the surface of a diamond, taken by physicist S. Tolansky.  Using chemical processes to attack the diamond surface, an etched surface was produced.  In Fig. 71, the microscopic blocks resemble mountainous chunks sticking out from the surface.  However, in Fig. 72 the features resemble caverns or hollows in a solid wall, with no blocks standing out.  Strangely, Fig. 72 is merely Fig. 71 turned upside down. 

Fig. 71 – The etched surface of a diamond. 

Fig. 72 – Another etched surface of a diamond. 
This figure is actually Fig. 70 turned upside down. 

The most interesting point is that there exists a turning point between the two interpretations, where the illusions morph into each other.  If one turns Fig. 71 or Fig. 72 slowly, there will be some intermediate position where the picture suddenly oscillates.  It jumps rapidly from blocks to caverns and back.  There will be two positions where this takes place. 

The illusion causes a serious scientific problem.  Which surface are we actually looking at?  Are we examining blocks or caverns?  Tolansky reported that he had to use additional optical techniques to find out. 

Shown below are a few classical examples of illusions due to the oscillation of attention.  An artist particularly famous for such paintings is Maurits Cornelis Escher.  As a child, he had an intensely creative side and an acute sense of wonder.  Escher often claimed to see shapes that he could relate to in the clouds.  Though people expressed the opinion that he possessed a mathematical brain, he never excelled in the subject at any stage during his schooling.

Fig. 73 – M. Escher’s “Convex and Concave”. 

Fig. 74 – M. Escher’s “Relativity”.
 

Fig. 75 – M. Escher’s “Belvedere”. 

Fig. 76 – A classic example: Schroder’s staircase. 
Which is front and which is back?