Burning ship fractal with generativepy

Martin McBride, 2020-10-28
Tags burning ship fractal
Categories generativepy generative art

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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 make_bitmap, Scaler
from generativepy.color import Color

BLACK = Color(0)

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
    return -1

def build_color_table(size):
    table = [Color.of_hsl(i/size, 1, 0.5) for i in range(size)]
    return table

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)

    colors = build_color_table(MAX_COUNT)

    for px in range(pixel_width):
        for py in range(pixel_height):
            x, y = scaler.device_to_user(px, py)
            count = calc(x, y)
            col = BLACK if count < 0 else colors[count]
            image.putpixel((px, py), col.as_rgb_bytes())

make_bitmap('burning-ship.png', paint, 800, 600)

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.

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