Fractal Geometry: The Gosper Island) (a) Write a function M-file gospe r (n) that will input a positive integer n and will produce a graphic of the nth generation of the Gosper island fractal, which is defined as follows: Generation zero is a regular hexagon (with, say, unit side lengths). To get from this to generation one, we replace each of the six sides on the boundary of generation zero with three new segments as shown. The first few generations of the Gosper island are shown.
(b) (Tessellations of the Plane) It is well known that the only regular polygons that can tessellate (or tile) the plane are the equilateral triangle, the square, and the regular hexagon (honeybees have figured this out). It is an interesting fact that any generation of the Gosper island can also be used to tessellate the plane, as shown Get MATLAB to reproduce each of tessellations that are shown.
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