gosper.py

import numpy as np
from matplotlib import pyplot as pp
from math import pi, sqrt


class Turtle:
    def __init__(self, angle_step):
        self.angle_step = angle_step

        self.direction = 0

        self.angles = []
        self.directions = []

    def left(self):
        self.direction -= 1

    def right(self):
        self.direction += 1

    def forward(self):
        self.angles.append(self.direction)
        self.directions.append(1)

    def backward(self):
        self.angles.append(self.direction)
        self.directions.append(-1)

    def produce(self):
        a = np.array(self.angles) * self.angle_step
        d = np.array(self.directions)

        dx = np.cos(a) * d
        dy = np.sin(a) * d

        return np.cumsum(dx), np.cumsum(dy)


def gosper(level):
    g = Gosper()
    g.A(level)
    return g.produce()


class Gosper:
    """L-system is:
    A -> A-B--B+A++AA+B-
    B -> +A-BB--B-A++A+B
    """

    def __init__(self):
        self.turtle = Turtle(pi / 3)

    def produce(self):
        return self.turtle.produce()

    def A(self, level):
        """A -> A-B--B+A++AA+B-"""
        if level == 0:
            self.turtle.forward()
        else:
            t = self.turtle
            level -= 1
            self.A(level)
            t.left()
            self.B(level)
            t.left()
            t.left()
            self.B(level)
            t.right()
            self.A(level)
            t.right()
            t.right()
            self.A(level)
            self.A(level)
            t.right()
            self.B(level)
            t.left()

    def B(self, level):
        """+A-BB--B-A++A+B"""
        if level == 0:
            self.turtle.forward()
        else:
            t = self.turtle
            level -= 1
            t.right()
            self.A(level)
            t.left()
            self.B(level)
            self.B(level)
            t.left()
            t.left()
            self.B(level)
            t.left()
            self.A(level)
            t.right()
            t.right()
            self.A(level)
            t.right()
            self.B(level)


def gosper_diagram(size, order, scale):
    from PIL import Image, ImageDraw

    xx, yy = gosper(order)
    xx *= scale
    yy *= scale

    xx += int(size / 2 - xx.mean())
    yy += int(size / 2 - yy.mean())

    image = Image.new("L", (size, size))
    draw = ImageDraw.Draw(image)

    draw.line(list(zip(xx, yy)), fill=255)
    # image.show()
    return np.asarray(image)


if __name__ == "__main__":
    print(gosper_diagram(512, 5, 4 * sqrt(1.5)))