logisticmap.py

#/usr/bin/env python

import numpy as np
import sys
import matplotlib.pyplot as plt

#Todo: add slider, make bifurication diagram

#
# An investigation into the Logistic map, and an introduction to matplotlib
#r = 2: 1 attractor
#r = 3: 2 attractors
#r = 3.449490: 4 attractors
#
# This phenonmenon is called period doubling, or bifurication. As we increase r, the periods will bifuricate, until we reach
# r = 3.569945672, or Feigenbaum's Constant: the brink of chaos
# This r gives the limiting accumulation of bifurications, the limit of of order, predictability. Beyond Feigenbaum's constant our logistical map falls to chaos
# map becomes chaotic, culminating in r = 4


def logistic(seed, r, times):
	y = []
	def quad_recur(seed, r, times):
		if times > 0:
			y.append(seed)
			new_seed = r*seed*(1 - seed)
			quad_recur(new_seed, r, times -1)
	quad_recur(seed, r,times)
	return y
			
def main(argv):
	iterations = int(argv[2])
	t = np.arange(0,iterations)
	y = logistic(float(argv[0]), float(argv[1]), iterations);  

	plt.plot(t,y)


	plt.ylabel('some numbers')
	plt.show()

if __name__ == '__main__':
	main(sys.argv[1:])