Burning ship fractal with generativepy

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

This article has been moved to my blog. Please refer to that article as it might be more up to date.

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.

See also

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

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