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What happens if you combine the Mandelbrot iteration with some randomness? In the 1990s several authors tried to understand it by computing numerically the probability of belonging to the Mandelbrot set when choosing randomly the parameters. More precisely, starting from a 2-dimensional array of boxes, each corresponding to a final pixel in the image, a random sampling of points are iterated through the Mandelbrot function. After repeating the computation for a billion points, one obtains a density plot where the regions corresponding to points most likely to diverge to infinity under iteration are rendered. We add a little quirk: at each iteration step we take the complex conjugate, turning the polynomial into an anti-holomorphic function and de facto forcing the dynamics to be more symmetric than otherwise it would be

MetaBrot Collection

Fire Lemon is a MetaBrot based on the distribution the orbits of 1 billion random points through repeated iterations of the polynomial 0.5 z + 0.6 z² - 0.2 z³ - 0.3 z⁴ - 0.4 z⁵

#40 Fire Lemon

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