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Two programming challenges


Mathematica Programming Challenge 1

Given several points in the plane, connect these points by line
segments, resulting in a connected polygonal line that passes through
all the points and does not intersect itself.  Arrange it so that the
line seems to spiral inwards.


Mathematica Programming Challenge 2

There are two rhombi, named after Penrose, which you can use to tile the
plane.  They both have the same edge length; the narrower rhombus has a
tip angle of Pi/5, and the wider rhombus has a tip angle of 2Pi/5.
Write a program that produces random (whatever that means) tesselations
of (part of) the plane, using these two shapes.

Will Self


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