Escher Fractal Exploration

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Time-30.svg

Objective: Create Escher like fractals.

Escher experimented with some simple self-similar objects. If you start with a square, and inscribe successive squares you will get a self-similar shape. One of his works is recreated below. Several resulting triangles were shaded in to make the image visually more interesting.

Escherfractal1.png

1. Copy the design to the right hand side.


We can go one step further and divide all triangles in two. This can easily be achieved by drawing both diagonal in the large square and the next smaller square. Alternate triangles were shaded. (This is also a copy of one of Escher's self-similar shapes.)


Escherfractal2.png


2. Copy the design to the right hand side.


More interesting patterns, which can be thought of as fractals, were created by repeatedly dividing squares in fourths:


Escherfractal3.png


3. Divide the bottom four squares into fourths.

4. Repeat this process on the picture in stage 2. You should get something like this:

Escherfractal4.png

5. Copy one of the patterns done by Escher onto the square below. Use shading to make the repeating pattern of the fractal visible. See for instance Visions of Symmetry, Pg. 315


Escherfractal4.png


Handin: A sheet with answers to all questions.