What is Self-Similarity?

What is Self-Similarity?

Self-similarity is defined as the geometrical resemblance between the parts of a shape and the shape as a whole.

The diagram below indicates four rectangles, the first two rectangles are similar in the strict mathematical sense ie. although there scales are different their proportions are the same. the second two sets of rectangles are NOT similar as their proportions are quite different.


The following diagrams are SELF-SIMILAR in that a part of the shape is representative of the whole shape.
Examples of Self-Similarity

A long row of candles: self-similarity induced by parallel mirrors. (Fractals, Chaos, Power Laws. M Schroeder 1991)
The chambered snail Nautilus follows a logarithmic spiral in its self-similar design Photo by Edward Weston (Fractals, Chaos, Power Laws. M Schroeder 1991)

Architectural examples of Self-Similarity

Castle del Monte, designed and built by the Holy Roman Emperor Frederick II (1194-1250), has a octagonal basic shape with 8 octagonal towers at each vertex. In plan this buliding can be seen to have self-similar properties (Fractals, Chaos, Power Laws. M Schroeder 1991). Try drawing the plan and see for your self.

Rokko Housing, I and II, an aerial view, Hyogo, Japan (Tadao Ando). Shows self-similar properties in the arrangement of the blocks
Self-similarity in the elevation of this housing block in Amsterdam
for more:
                 Ph.D. in Technologies for the Exploitation
                 of the Cultural Heritage .
                 Senior Lecturer in the Dept. of Architecture

                 College of Engineering , University of Mosul 
                 Mosul - Iraq .

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