SharedDragon Fractal.ipynbOpen in CoCalc
Dragon Fractal in Python

The Dragon Fractal¶

import numpy as np
import matplotlib.pyplot as plt

s = ''

def replace(x):
return x.replace('V','m').replace('M','V').upper()[::-1]

def dragonNext(x):
return x + 'V' + replace(x)

def iterateDragon(N):
x = s
for i in range(N):
x = dragonNext(x)
return x

def nextDir(curr,dir):
if curr == 'E' and dir == 'V':
return 'S'
if curr == 'W' and dir == 'V':
return 'N'
if curr == 'S' and dir == 'V':
return 'W'
if curr == 'N' and dir == 'V':
return 'E'
if curr == 'E' and dir == 'M':
return 'N'
if curr == 'W' and dir == 'M':
return 'S'
if curr == 'S' and dir == 'M':
return 'E'
if curr == 'N' and dir == 'M':
return 'W'

def strToDir(x):
lst = 'N'
for char in x:
lst += nextDir(lst[-1],char)
return lst

def points(N):
str = iterateDragon(N)
dir = strToDir(str)
x,y = [0],[0]
for char in dir:
if char == 'N':
x += [x[-1]]
y += [y[-1]+1]
if char == 'E':
x += [x[-1]+1]
y += [y[-1]]
if char == 'S':
x += [x[-1]]
y += [y[-1]-1]
if char == 'W':
x += [x[-1]-1]
y += [y[-1]]
return np.array(x),np.array(y)

def dragon(N):
x,y = points(N)
plt.plot(x,y,color='black')

dragon(15)