This is actually the first zoom of a different fractal type so. Plot this like the mandelbrot set and you get the burning ship fractal.
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The following image is the standard power 2 burning ship fractal rendered using cpm smooth coloring.
Burning ship fractal. The burning ship fractal. For example the points shown in black in the center of the form dont ever diverge to infinity they either oscillate or converge to a singe value. The points shown in light grey diverge very quickly.
The burning ship is a non analytic cousin of the mandelbrot. The difference between this calculation and that for the mandelbrot set is that the real and imaginary components are set to their respective absolute values before squaring at each iteration. The formula that the burning ship fractal uses is z a i b where a and b are the real and imaginary parts respectively.
You can see that this will grow towards infinity and therefore is outside of the burning ship set. Some would say an ugly cousin but i think it certainly has its charms. This is one of the creepiest and yet stunningly gorgeous fractals ever.
The burning ship fractal is a slight variant on the mandelbrot set fractal. The grey level assigned to each point c x c y is determined by how fast the series tends to infinity. The mapping is non analytic because its real and imaginary parts do not obey the cauchyriemann equations.
The basic mandelbrot fractal formula is zz2c. The burning ship fractal formula is zabsz2c. The deepest and first ever hd deep zoom animation into the burning ship fractal.
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