Dragon curve

main.py

# The equations are from: https://en.wikipedia.org/wiki/Dragon_curve
# I start with a line segment (0, 0) to (1, 0) and map the endpoints through f1 and f2.
# Then I have two segments (0, 0) to (0.5, 0.5) and (0.5, 0.5) to (1, 0).
# The endpoints are repeatedly mapped in the for-loop.

import matplotlib.pyplot as plt
import numpy as np

def f1(x):
    return 1. / np.sqrt(2) * (
        np.array([[np.cos(np.pi/4), -np.sin(np.pi/4)], 
                  [np.sin(np.pi/4), np.cos(np.pi/4)]])
    ).dot(x)

def f2(x):
    return 1. / np.sqrt(2) * (
        np.array([[np.cos(3*np.pi/4), -np.sin(3*np.pi/4)], 
                  [np.sin(3*np.pi/4), np.cos(3*np.pi/4)]])
    ).dot(x) + np.array([[1], [0]])

segments = [np.array([[1, 0], [0, 0]])]
for itr in range(10):
    nsegments = []
    for seg in segments:
        nsegments.append(f1(seg))
        nsegments.append(f2(seg))
    segments = nsegments
    
plt.plot(np.array(segments)[:, 0, :].T, np.array(segments)[:, 1, :].T, 'k-')