main

import numpy as np 
import matplotlib.pyplot as plt 
import matplotlib.animation as animation
from numba import jit

# Julia set
# https://en.wikipedia.org/wiki/Julia_set#Quadratic_polynomials

@jit
def JuliaSet(N,Nx,Ny,z,c):
    M = Nx*Ny
    Z = z*np.ones(M,dtype=complex)
    A = np.zeros(M)

    for i in range(M):
        for n in range(N):
            if np.abs(Z[i]) < 2:
                Z[i] = Z[i]**2 + c
            else:
                A[i] = n
                break    
        
    A = A.reshape(Ny,Nx)
    return A

N = 200
h = 0.001

xlm = [-1.6,1.6]
ylm = [-1.2,1.2]

c = -0.763 + 0j

x  = np.arange(xlm[0],xlm[1]+h,h)
y  = np.arange(ylm[0],ylm[1]+h,h)
Nx = len(x)
Ny = len(y)

xx, yy = np.meshgrid(x,y)
z  = (xx + yy*1j).flatten()

A = JuliaSet(N,Nx,Ny,z,c)

C = c - 0.0025*np.arange(0,200)*1j

cmap = 'hot'

interpolation = 'spline16'

plt.close('all')
fig = plt.figure()

im = plt.imshow(A,extent=[xlm[0],xlm[1],ylm[0],ylm[1]],cmap=cmap,interpolation=interpolation)
plt.clim([0,100])
plt.axis('off')

interval = 120

def update(i):
    c = C[i]
    A = JuliaSet(N,Nx,Ny,z,c)
    im.set_data(A)

ani = animation.FuncAnimation(fig, update, frames=len(C),interval=interval)
ani.save('c=%+.3f%+.3fi' % (c.real,c.imag)+'.mp4', writer="ffmpeg")