import math as m
import numpy as np
import matplotlib.pyplot as plt
import scipy.special as sp
# import matplotlib.animation as animation
def draw_frame(n,filename,line_color):
	fig = plt.figure()
	plt.axes([0.02,0.13,0.9,0.8])
	plt.hold(True)
	plt.xlim(-1.5,1.5)
	plt.ylim(-4,2)
	# Set up the spines
	ax = plt.gca()
	ax.spines['right'].set_color('none')
	ax.spines['top'].set_color('none')
	ax.xaxis.set_ticks_position('bottom')
	ax.spines['bottom'].set_position(('data',0))
	ax.yaxis.set_ticks_position('left')
	ax.spines['left'].set_position(('data',0))
	# Set up the label
	ax.text(0.5,-2,'N='+str(n),fontsize=24,color=line_color)

	Q = []
	# Draw the original function (ORG) curve
	X = np.arange(-0.999, 1.5, 0.001)
	ORG = np.log(X+1)
	a = plt.plot(X, ORG, '-', color='black', lw=3)
	Q.append(a)
	# Draw the approximation function (APPR) curve
	X = np.arange(-1.5, 1.5, 0.001)
	i=1
	APPR = (-1)**(i+1)*(X**i)/i
	while (i<n):
		i = i+1
		APPR = APPR+(-1)**(i+1)*(X**i)/i
	a = plt.plot(X, APPR, '-', color=line_color, lw=3)
	Q.append(a)
	
	plt.savefig(filename)

draw_frame(1,'frame01.jpg','#b30000')
draw_frame(2,'frame02.jpg','#00b300')
draw_frame(3,'frame03.jpg','#0000b3')
draw_frame(4,'frame04.jpg','#b3b300')
draw_frame(5,'frame05.jpg','#00b3b3')
draw_frame(6,'frame06.jpg','#b300b3')
draw_frame(7,'frame07.jpg','#b3b3b3')
draw_frame(8,'frame08.jpg','#3300b3')
draw_frame(9,'frame09.jpg','#33b300')
draw_frame(10,'frame10.jpg','#0033b3')
draw_frame(15,'frame11.jpg','#b3b333')
draw_frame(20,'frame12.jpg','#334433')
draw_frame(45,'frame13.jpg','#ff0000')
draw_frame(100,'frame14.jpg','#0000ff')

# To generate the final GIF file, use the shell command:
# convert -antialias -loop 0 -delay 100 -compress LZW frame* Logarithm_GIF.gif