Newton Basin Project

egoughnour

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This will have smoothing and histogram coloring if possible

This Python template lets you get started quickly with a simple working example. If it is your first contribution then you should have a look at the Getting Started document.

The source code is on GitHub, please feel free to come up with proposals to improve it.

Hands-on Demo

Is 7 in the basin of attraction of any roots of the cubic z(z-1)(z+1)

from PIL import Image, ImageDraw
from basin import cubicbrot, MAX_ITER
from collections import defaultdict
from math import floor, ceil
def linear_interpolation(color1, color2, t):
    return color1 * (1 - t) + color2 * t 
# Image size (pixels)
WIDTH = 600
HEIGHT = 400
# Plot window
RE_START = -2
RE_END = 1
IM_START = -1
IM_END = 1
histogram = defaultdict(lambda: 0)
values = {}
im = Image.new('RGB', (WIDTH, HEIGHT), (0, 0, 0))
draw = ImageDraw.Draw(im)
for x in range(0, WIDTH):
    for y in range(0, HEIGHT):
        # Convert pixel coordinate to complex number
        c = complex(RE_START + (x / WIDTH) * (RE_END - RE_START),
                    IM_START + (y / HEIGHT) * (IM_END - IM_START))
        # Compute the number of iterations
        m = cubicbrot(c)
        values[(x, y)] = m
        if m < MAX_ITER:
            histogram[floor(m)] += 1
total = sum(histogram.values())
hues = []
h = 0
for i in range(MAX_ITER):
    h += histogram[i] / total
    hues.append(h)
hues.append(h)
im = Image.new('HSV', (WIDTH, HEIGHT), (0, 0, 0))
draw = ImageDraw.Draw(im)
for x in range(0, WIDTH):
    for y in range(0, HEIGHT):
        m = values[(x, y)]
        # The color depends on the number of iterations    

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2/3 Colored By Iterations

This will have smoothing and histogram coloring if possible

Hands-on Demo

Template Resources

Visual and Interactive Content

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