...surfaces.

On a surface, a geodesic is the analogue of a straight line in the plane; travelling on the geodesic within the surface, we would believe we were following the straightest path possible. For instance, the geodesics on a sphere are the great circles.

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...mathematics,

To see Escher's version of another famous creation of Penrose (when he was fourteen!) and his father click Ascending and Descending

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...subsequences.

Actually, there are uncountably many choices; this is a term that comes from the study of comparing sizes of infinite sets. Uncountable means that the set cannot be placed in one-to-one correspondence with the set of integers.

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...similarities.

We usually think of a transformation 192#192 as acting on points T(x,y). However, we also use the notation T(A) for a subset 590#590 to mean the set of all points T(x,y) where (x,y) belongs to A.

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...Hokusai.

On display in the Metropolitan Museum of Art in New York; this artwork was used by Mandelbrot as an example of ``fractal artistry''.

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...

1. The first three problems are taken from L-systems tutorial at Australian National University.

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