Martin McBride, 2020-10-28

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.

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:

Here is the full code for the burning ship fractal:

from generativepy.bitmap import make_bitmap, Scaler from generativepy.color import Color MAX_COUNT = 200 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.

Copyright (c) Axlesoft Ltd 2020