%matplotlib inline

import numpy as np
import matplotlib.pyplot as plt

from matplotlib import animation, rc
from IPython.display import HTML

fig, ax = plt.subplots();

ax.set_xlim((0,1))
ax.set_ylim((0,0.866))
ax.set_aspect(0.866)
sct = ax.scatter([],[])
initPoints = [[0,0], [1,0], [0.5,0.866]]
data = []
r = 0.5

plt.close('all')

def nextPoint(point,init,choice):
    x1,y1 = point
    x2,y2 = init[choice]
    return (x1*(1-r)+x2*r, y1*(1-r)+y2*r)

N = 1000
start = [0.5,0]
data.append(start)
for i in range(N-1):
    k = np.random.randint(0,len(initPoints))
    data.append(nextPoint(data[-1],initPoints,k))

def animate(i,data):
    x = data[i][0]
    y = data[i][1]
    array = sct.get_offsets()
    array = np.vstack([array,[x,y]])
    sct.set_offsets(array)
    return sct,

anim = animation.FuncAnimation(fig, animate, frames=1000, interval=30, blit=True, fargs=(data,), repeat=False)

HTML(anim.to_html5_video())