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.

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.

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