"""Barnsley Fern fractal generation"""
import random
import array
from PIL import Image
class Barnsley:
"""Generate Barnsley like fractals using affine transforms"""
def __init__(self, nr_points, coefficients="fern"):
self.nr_points = nr_points
#Initial (starting point)
self.x = 0.0
self.y = 0.0
# Store the fractal points
self.point_x = []
self.point_y = []
# Select the set of coefficients to use
if coefficients == "fern":
self.probability_factors = [0.01, 0.85, 0.07, 0.07]
self.a = [0, 0.85, 0.20, -0.15]
self.b = [0, 0.04, -0.26, 0.28]
self.c = [0, -0.04, 0.23, 0.26]
self.d = [0.16, 0.85, 0.22, 0.24]
self.e = [0, 0, 0, 0]
self.f = [0, 1.6, 1.6, 0.44]
elif coefficients == "tree":
self.probability_factors = [0.05, 0.4, 0.4, 0.15]
self.a = [0.0, 0.42, 0.42, 0.1]
self.b = [0.0, -0.42, 0.42, 0.0]
self.c = [0.0, 0.42, -0.42, 0.0]
self.d = [0.5, 0.42, 0.42, 0.1]
self.e = [0.0, 0.0, 0.0, 0.0]
self.f = [0.0, 0.2, 0.2, 0.2]
elif coefficients == "sierpinsky":
self.probability_factors = [0.33, 0.33, 0.34]
self.a = [0.5, 0.5, 0.5]
self.b = [0.0, 0.0, 0.0]
self.c = [0.0, 0.0, 0.0]
self.d = [0.5, 0.5, 0.5]
self.e = [1.0, 1.0, 50.0]
self.f = [1.0, 50.0, 50.0]
elif coefficients == "custom":
self.probability_factors = [0.04, 0.8, 0.08, 0.08]
self.a = [0, 0.7, 0.20, -0.2]
self.b = [0, 0.035, -0.29, 0.28]
self.c = [0, -0.04, 0.23, 0.26]
self.d = [0.16, 0.8, 0.22, 0.25]
self.e = [0, 0, 0, 0]
self.f = [0, 1.6, 1.6, 0.44]
self.nr_transforms = len(self.probability_factors)
# Cumulative sum of the probabilty factors,
# this defines the intervals corresponding to each transform
self.cumulative_probabilities = [0] * (self.nr_transforms + 1)
for i in range(1, len(self.cumulative_probabilities)):
self.cumulative_probabilities[i] = self.cumulative_probabilities[i - 1] + \
self.probability_factors[i - 1]
def select_transform(self):
"""Randomly select an affine transform"""
rnd = random.random()
for i in range(self.nr_transforms):
if self.cumulative_probabilities[i] <= rnd <= self.cumulative_probabilities[i + 1]:
self.current_transform = i
break
def next_point(self):
"""Get the next point of the fractal"""
self.select_transform()
x_new = self.a[self.current_transform] * self.x + self.b[self.current_transform] * self.y + self.e[self.current_transform]
y_new = self.c[self.current_transform] * self.x + self.d[self.current_transform] * self.y + self.f[self.current_transform]
self.x = x_new
self.y = y_new
self.point_x.append(x_new)
self.point_y.append(y_new)
def generate_points(self):
"""Generate all the fractal points"""
for _ in range(self.nr_points):
self.next_point()
# Bounding box for the fractal
self.x_min = min(self.point_x)
self.x_max = max(self.point_x)
self.y_min = min(self.point_y)
self.y_max = max(self.point_y)
def main():
"""Generate and the save as a PNG image a Barnsley Fern"""
# Initialize the fractal data
nr_points = 100000
fern = Barnsley(nr_points)
fern.generate_points()
# Define the image size and scale factor for the fractal data
width, height = 500, 500
scale = min([height/(fern.y_max - fern.y_min), width/(fern.x_max - fern.x_min)]) * 0.9
# Initialize an array that will store the image pixel data
image_data = array.array('B', [255, 255, 255] * width * height)
# For every point of the fractal data, transform the point in the image space
# and fill the pixel color
for i in range(nr_points):
x = int((fern.point_x[i] - fern.x_min) * scale) + int((width - (fern.x_max - fern.x_min) * scale)/2)
y = -int((fern.point_y[i] - fern.y_min) * scale) - int((height - (fern.y_max - fern.y_min) * scale)/2)
index = 3 * (y * width + x)
image_data[index] = 0
image_data[index + 1] = 255
image_data[index + 2] = 0
# Show and save the image
img = Image.frombytes("RGB", (width, height), image_data.tobytes())
img.show("Barnsley's Fern")
img.save("barnsley_fern.png")
if __name__ == "__main__":
# execute only if run as a script
main()
