def sierpinski_step(triangle_vertices):
n = len(triangle_vertices) # 3
midpoints = [
midpoint(*pair_vertices)
for pair_vertices in combinations(triangle_vertices, 2)
]
res = []
for i, pair_midpoints in enumerate(combinations(midpoints, 2)):
# res += (*pair_midpoints, triangle_vertices[(i+2)%3])
res += (*pair_midpoints, triangle_vertices[i])
return res
def brownian_island(frm, to, variance, scale, n):
if n == 0:
return [(frm, to)]
m = midpoint(frm, to)
rand_height = normal(0, sqrt(variance))
rand_width = normal(0, sqrt(variance))
m = m[0] + rand_width, m[1] + rand_height
points = []
points += brownian_island(frm, m, variance / scale, scale, n - 1)
points += brownian_island(m, to, variance / scale, scale, n - 1)
return points
def brownian_bridge(frm, to, variance, scale):
points = []
if abs(to[0] - frm[0]) < TOLERANCE:
points += [(frm, to)]
else:
m = midpoint(frm, to)
rand_height = normal(0, sqrt(variance))
m = m[0], m[1] + rand_height
points += brownian_bridge(frm, m, variance / scale, scale)
points += brownian_bridge(m, to, variance / scale, scale)
return points
def horizontal_split(bottom_left, top_right):
top_left, bottom_right = other_corners(bottom_left, top_right)
return [midpoint(bottom_left, top_left), midpoint(bottom_right, top_right)]
def vertical_split(bottom_left, top_right):
top_left, bottom_right = other_corners(bottom_left, top_right)
return [midpoint(bottom_left, bottom_right), midpoint(top_left, top_right)]
def center(self):
return midpoint(self._bottom_left, self._top_right)
def get_H_shape_lines(uc, lc):
"return list of points to draw for the H shape given the upper corner and the lower corner"
return [[midpoint(uc[0], lc[0]),
midpoint(uc[1], lc[1])], [uc[0], lc[0]], [uc[1], lc[1]]]