File:C0 seq cauchy in l2.gif

#!/usr/bin/env python
# -*- coding: utf-8 -*- 
'''
Este trabalho está licenciado sob a Licença Creative Commons 
Atribuição-CompartilhaIgual 4.0 Internacional. Para ver uma cópia desta licença,
visite https://creativecommons.org/licenses/by-sa/4.0/ ou envie uma carta 
para Creative Commons, PO Box 1866, Mountain View, CA 94042, USA.
'''

from __future__ import division
import numpy as np
import matplotlib.pylab as plt
import matplotlib.animation as animation

fig = plt.figure(figsize = (4,3), dpi=100, frameon=False)
ax = plt.subplot(1,1,1)
plt.axis('off')

#x - axis
ax.set_xlim((-1.5,1.5))
plt.arrow(-1.5,0,3,0,head_width=0.075, length_includes_head=True, facecolor='black')
plt.text(1.25, -0.2, r'$x$', fontsize=14)

#y- axis
ax.set_ylim((-0.25,1.75))
plt.arrow(0,-0.25,0,2,head_width=0.075, length_includes_head=True, facecolor='black')
plt.text(-0.2, 1.5, r'$y$', fontsize=14)

line1, = plt.plot([-1,0],[0,0],'b-', linewidth=1.5)
line2, = plt.plot([0,1],[0,1],'b-', linewidth=1.5)
line3, = plt.plot([1,1],[1,1],'b-', linewidth=1.5)
point1, = plt.plot(-1,0,'bo', markersize=4)
point2, = plt.plot(0,0,'bo', markersize=4)
point4, = plt.plot(1,1,'bo', markersize=4)

plt.plot([1,1],[-0.025,1],'k--', alpha=0.25)
plt.plot([-0.025,1],[1,1],'k--', alpha=0.25)
plt.text(0.95,-0.15,'$1$')
plt.text(-0.15,0.95,'$1$')

t = plt.text(-1,1,'')

def init():
    line1.set_color('blue')

    line2.set_color('blue')
    line2.set_xdata([0,1])

    line3.set_color('blue')
    line3.set_xdata([1,1])

    point1.set_color('blue')
    point2.set_marker('')
    point4.set_color('blue')
    t.set_text(r'$y = f_n(x)$')

    return line1, line2, line3, point1, point2, point4

def run(n):
    i = (1.75)**n
    if (n <= 12):
        line2.set_xdata([0,1/i])
        line2.set_marker('')

        line3.set_xdata([1/i,1])
    else:
        line1.set_color('red')

        line3.set_xdata([0,1])
        line3.set_color('red')

        line2.set_color('red')
        line2.set_xdata([0,0])
        line2.set_ydata([1,1])
        line2.set_marker('o')
        line2.set_markersize(4)
        line2.set_markerfacecolor('white')

        point1.set_color('red')
        point2.set_marker('o')
        point2.set_markersize(4)
        point2.set_markerfacecolor('red')
        point4.set_color('red')

        t.set_text(r'$f_n\to f\,\notin\,C^0$')

    return line1, line2, line3, point1, point2, point4

im_ani = animation.FuncAnimation(fig, run, np.arange(0,20), init_func=init, interval=100, blit=False)
im_ani.save('c0_seq_cauchy_in_l2.gif',writer='imagemagick',fps=1)