'''
Barnsley fern
'''

import time
import numpy as np
import pylab as plt
import matplotlib
matplotlib.use('Agg')

ax_lims = [-6,-0.5,6,9.0]

M1 = np.array([[0,0],[0,0.16]])
M2 = np.array([[0.85,0.04],[-0.04,0.85]])
M3 = np.array([[0.20,-0.26],[0.23,0.22]])
M4 = np.array([[-0.15,0.28],[0.26,0.24]])
def T1(x): return M1@x
def T2(x): return M2@x+np.array([0,1.6])
def T3(x): return M3@x+np.array([0,1.6])
def T4(x): return M4@x+np.array([0,0.44])
Ts = [T1,T2,T3,T4]

X = np.zeros((2,10**6))

for k in range(X.shape[1]-1):
    X[:,k+1] = Ts[np.random.randint(0,4)](X[:,k])

# [xmin, xmax, ymin, ymax]
ax_lims = [X[0,:].min()-0.5, X[0,:].max()+0.5,
        X[1,:].min()-0.5,X[1,:].max()+0.5]

t = [int(k) for k in np.round(2**np.linspace(0,19.9315,100) )]
for k in t:
    fig=plt.figure(figsize=(8,8))
    ax = plt.gca()
    ax.set_facecolor('k')
    ax.set_xticks([])
    ax.set_yticks([])
    plt.plot(X[0,0:k+1],X[1,0:k+1],'.',ms=1,c='#39ff14')
    plt.axis(ax_lims)

    plt.savefig('./t'+str(k+1)+'.png',dpi=100,facecolor='k')
    plt.close(fig)