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
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 MAX_COUNT = 256 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, counts.shape)) 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, counts.shape, 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.
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
scaler = Scaler(pixel_width, pixel_height, width=0.1, startx=-1.8, starty=-0.09)
These parameters zoom in on the new area.
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