#! /usr/bin/env python
"""
 Sierpinski.py is a program which plot the Sierpinski triangle, which is a  fractal

 One can generate the fractal pattern by following the prescription below:
 [1] Use the three (x,y) vertex points: (-1,0), (0, %3 ), and (1,0) in a plane to 
     form a triangle. [2] Starting from the origin (0,0) plot a point.
 [3] Randomly select any one of the 3 vertex points.
 [4] Move half the distance from your current position to the selected vertex.
 [5] Plot the new current position. [6] Repeat from step 3.


 This program demonstrates the fractal nature show the repeating pattern at different scales

 Paul Eugenio
 Florida State University
 PHZ4151C
 
 29 Jan 2019
"""

from __future__ import division, print_function
from math import sqrt
from matplotlib.pyplot import scatter, show, figure, xlim, ylim
import numpy as np

# The plotting point [x,y] starting at 0,0
plotPoint = [0,0]

# Create a list of 3 [x,y] points, one for of the triangle's vertices
triVertex = [[-1,0],[0,sqrt(3)],[1,0]]    

# Number of plotting points (many ponts are needed for fractal zooming)
N = 200000

# Lists for storing plotting data
x = []
y = []


for i in range(N):
    # Find a random point from {0,1,2}
    r = np.random.randint(3)

    # Creating a plotting point halfway between the current 
    # point and a randomly selected vertex
    plotPoint = [(plotPoint[0] + triVertex[r][0])/2, (plotPoint[1] + triVertex[r][1])/2]
    x += [plotPoint[0]]
    y += [plotPoint[1]]
    
#
# Create two figures for plotting: [1] the whole fractal, 
# [2] a zoomed in region exhibiting the fractal nature
#
fig1 = figure(1) 
scatter(x,y, s=0.1)
fig1.show()

fig2 = figure(2) 
scatter(x,y, s=0.1)

# Zoom in to a small corner of the triangle 
# to observe the repeating fractal nature
xlim(0.94, 1)
ylim(0, 0.04)

fig2.show()

# Stop program from automatically ending 
raw_input("Enter [return] to exit")