Add IFS in python

CONTRIBUTORS.md

@@ -42,9 +42,10 @@ This file lists everyone, who contributed to this repo and wanted to show up her
 - Christopher Milan
 - Vexatos
 - Raven-Blue Dragon
-- Björn Heinrichs 
+- Björn Heinrichs
 - Olav Sundfør
 - Ben Chislett
 - dovisutu
 - Antetokounpo
 - Akash Dhiman
+- Jonathan D. B. Van Schenck

contents/IFS/IFS.md

@@ -128,6 +128,8 @@ Here, instead of tracking children of children, we track a single individual tha
 {% method %}
 {% sample lang="jl" %}
 [import:4-17, lang:"julia"](code/julia/IFS.jl)
+{% sample lang="py" %}
+[import:5-12, lang:"python"](code/python/IFS.py)
 {% endmethod %}
 
 If we set the initial points to the on the equilateral triangle we saw before, we can see the Sierpinski triangle again after a few thousand iterations, as shown below:
@@ -180,6 +182,8 @@ In addition, we have written the chaos game code to take in a set of points so t
 {% method %}
 {% sample lang="jl" %}
 [import, lang:"julia"](code/julia/IFS.jl)
+{% sample lang="py" %}
+[import, lang:"python"](code/python/IFS.py)
 {% endmethod %}
 
 ### Bibliography

contents/IFS/code/python/IFS.py

@@ -0,0 +1,34 @@
+from random import random, choice
+from math import sqrt, sin, cos, pi
+
+# This generator simulates a "chaos game"
+def chaos_game(n, shape_points):
+    # Initialize the starting point
+    point = [random(), random()]
+
+    for _ in range(n):
+        # Update the point position and yield the result
+        point = [(_p + _s) / 2 for _p, _s in zip(point, choice(shape_points))]
+        yield point
+
+# This function generates the shape points for an N-gon inscribed inside a
+#  unit circle, with one of the edges oriented along the bottom
+def ngon_shape_points(N):
+    # Exterior N-gon angle
+    phi = 2 * pi / N
+
+    # Offset to put an edge at the bottom
+    delta = (pi + phi) / 2
+
+    return [[cos(- delta - m * phi), sin(- delta - m * phi)] for m in range(N)]
+
+# This will generate a Sierpinski triangle with a chaos game of n points for an
+# initial equilateral triangle inscribed on a unit circle. The shape points are:
+#     A = (-sqrt(3)/2, -0.5)
+#     B = (       0.0,  1.0)
+#     C = ( sqrt(3)/2, -0.5)
+# It will output the file sierpinski.dat, which can be plotted after
+shape_points = ngon_shape_points(3)
+with open("sierpinski.dat", "w") as f:
+    for point in chaos_game(10000, shape_points):
+        f.write("{0},{1}\n".format(*point))