MA-351 Homework 4
Due at 9:50 in class, Tuesday October 26, 1999
Calculations necessary for these problems may be done either by
hand or with Maple.
Solutions may be submitted in person in class,
or you may email an ASCII text,
Maple Worksheet (.mws),
html, or postscipt/pdf-formatted document to
me (kaltofen@math.ncsu.edu).
Note my office hours on my schedule.
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For the variant of Fibonacci's rabbits' problem of homework 1, give
a Lindenmayer system that models the growth.
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Consider a fractal called the Sierpinski gasket. You start with
an equilateral triangle. Remove the equilateral triangle formed
by the midpoints of the three edges. This leaves 3 equilateral
triangles of the same size at the corners. Recur the procedure
with these triangles.
Compute the remaining area (drawn in black in the above
picture) as a fraction of
the area of the original triangle when this procedure is continued to
infinity.
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DMM §3.6, Problem 13, page 168.
Note that your coloring also needs to include the
country "11" surrounding countries 1-10.