Burning ship fractal with generativepy

Martin McBride, 2021-06-15
Tags burning ship fractal
Categories generativepy generative art

The burning ship fractal is another famous fractal that can be implemented easily with generativepy.

Like the Mandelbrot set, the burning ship is an escape-time fractal.

Burning ship formula

The burning ship equations are similar to the Mandelbrot equations:

xnext = x*x - y*y + c1
ynext = 2*abs(x*y) + c2

Where c1 and c2 are two constant values.

The difference compared to the Mandelbrot equations in that the ynext equation uses abs(x*y) rather than just x*y. The absolute value is the positive size of the number, ignoring it's sign. So abs(3) is 3, abs(-3) is also 3.

Here is the image created:

The full code

Here is the full code for the burning ship fractal:

from generativepy.bitmap import Scaler
from generativepy.nparray import (make_nparray_data, make_npcolormap, save_nparray,
                                  load_nparray, save_nparray_image, apply_npcolormap)
from generativepy.color import Color
import numpy as np


def calc(c1, c2):
    x = y = 0
    for i in range(MAX_COUNT):
        x, y = x*x - y*y + c1, abs(2*x*y) + c2
        if x*x + y*y > 4:
            return i + 1
    return 0

def paint(image, pixel_width, pixel_height, frame_no, frame_count):
    scaler = Scaler(pixel_width, pixel_height, width=3.2, startx=-2, starty=-1.8)

    for px in range(pixel_width):
        for py in range(pixel_height):
            x, y = scaler.device_to_user(px, py)
            count = calc(x, y)
            image[py, px] = count

def colorise(counts):
    counts = np.reshape(counts, (counts.shape[0], counts.shape[1]))

    colormap = make_npcolormap(MAX_COUNT+1,
                               [Color('black'), Color('red'), Color('orange'), Color('yellow'), Color('white')],
                               [16, 8, 32, 128])

    outarray = np.zeros((counts.shape[0], counts.shape[1], 3), dtype=np.uint8)
    apply_npcolormap(outarray, counts, colormap)
    return outarray

data = make_nparray_data(paint, 800, 600, channels=1)

save_nparray("/tmp/temp.dat", data)
data = load_nparray("/tmp/temp.dat")

frame = colorise(data)

save_nparray_image('burning-ship.png', frame)

As well as changing the formula we have also slighlty adjusted the area of the user space (in the call to Scaler), to better fit the image. In adition we have used a red, orange, and yellow colour scheme.

Zooming in

Just like the Mandebrot set, the burning ship fractal contains miniature "copies" of itself at various places. They aren't actual copies, they have different but similar shapes.

In fact, the small black blob to the left of the main feature is actually more impressive, and is the real reason for the name. Here is what it looks like zoomed in:

Toobtain this image, we can use the code above by simple altering the scaler parameters in the paint function:

    scaler = Scaler(pixel_width, pixel_height, width=0.1, startx=-1.8, starty=-0.09)

These parameters zoom in on the new area.

If you found this article useful, you might be interested in the book Computer Graphics in Python or other books by the same author.


Popular tags

2d arrays abstract data type alignment and animation arc array arrays bezier curve built-in function callable object circle classes close closure cmyk colour comparison operator comprehension context context manager conversion creational pattern data types design pattern device space dictionary drawing duck typing efficiency else encryption enumerate fill filter font font style for loop function function composition function plot functools game development generativepy tutorial generator geometry gif gradient greyscale higher order function hsl html image image processing imagesurface immutable object index inner function input installing iter iterable iterator itertools l system lambda function len line linspace list list comprehension logical operator lru_cache magic method mandelbrot mandelbrot set map monad mutability named parameter numeric python numpy object open operator optional parameter or partial application path polygon positional parameter print pure function pycairo radial gradient range recipes rectangle recursion reduce rgb rotation scaling sector segment sequence singleton slice slicing sound spirograph sprite square str stream string stroke subpath symmetric encryption template text text metrics tinkerbell fractal transform translation transparency tuple turtle unpacking user space vectorisation webserver website while loop zip