Use the python programming language to write the code for this work. In the complex plane, the
Question:
Use the python programming language to write the code for this work.
In the complex plane, the Heighway dragon is the limit of the iterated function system(IFS) de ned
by the following transformations
f1(z) = (1 + i)z
2
f2(z) = 1 −
(1 − i)z
2
with the initial set of points S0 = {0, 1}.
(a) Using an initial value of z0 = 0 perform a few iterations of the two transformations above and store
the results of each iteration in an array zvals. Plot the =(zvals) versus <(zvals) and investigate
your results after each iteration. What happens to the line segments?
(b) The twindragon can be constructed by placing two Heighway dragon curves back-to-back. It is
the limit of the following IFS
f1(z) = (1 + i)z
2
f2(z) = 1 −
(1 + i)z
2
with the initial set of points S0 = {0, 1, 1 − i}
(c) The terdragon is the limit of the following IFS
f1(z) =λz
f2(z) = i
√
3
z + λ
f3(z) =λz + λ
∗
where λ =
1
2 −
i
2
√
3
and λ
∗ =
1
2 +
i
2
√
3
. Repeat the procedure in (i) and explain your results.
Expert Answer:
Heres the python code to visualize the Heighway dragon fractal using matplotlib import numpy as np i... View the full answer
