Dilation Exploration

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Objective: Learn to recognize similarity transformations.

For each print, discuss the symmetries. Find any isometries (rotations, for example) as well as any similarity transformations.

  1. Path of Life II (Visions of Symmetry pg. 311)
  2. Path of Life III (Visions of Symmetry pg. 316)
  3. Butterflies (Color) (Visions of Symmetry pg. 305)
  4. Sketch #65 (Moths) (Visions of Symmetry pg. 167)

Look at Escher's Regular Division of the Plane by Similar Figures patterns. These patterns (and Sketch #65 (Moths)) are all based on the following pattern, which has a dilation-rotation by a factor of <math>\frac{1}{\sqrt{2}}</math> and angle of 45°:


5. Sketch this square "scaffolding" on top of each of Escher's geometric patterns.