![]() Mandelbrot_graph = Image.new('RGB', (Width, Height), (0, 0, 0)) Here is a small snippet of code: max_iter = 100 You can also choose the location of the image you are creating. Essentially, every pixel takes a complex numbered value, and you then apply the iterative function to each pixel. I really like this algorithm because I find it super intuitive. Unfortunately, you cannot zoom in and have the image change. I have used this link to write a script on python that generates images of Julia sets. The perturbation techniques can be applied to other escape time fractals like the Burning Ship, but series approximation is tricky with non-analytic folding from $|.|$. There is a beta version for Windows x86_64: (I tried it in Wine on Linux but it did not work properly). Some nonspecific information on how it works was posted by its author at. Though, reading the documentation it may pause occasionally to recache some reference orbits or so. retinamandelbrot is an iOS app (which has just left beta) that claims to combine smooth zooming with deep zooms, but I haven't tried it myself. In 2013 K.I.Martin popularized perturbation techniques, which allow using low (machine) precision numbers for most of the calculations, and series approximation reduces the calculations required still further: I currently maintain some software that uses these techniques: It does have a progressive display (low resolution preview is gradually refined) but that isn't smooth zooming like xaos. ![]() Mandelbrot set deep zooming with arbitrary high precision (emulated in software using libraries like MPFR) for every pixel is prohibitively expensive. It does not support deep zooms, and the 53-64 bits of (long) double precision are quickly exhausted when zooming in (you need at least enough bits to distinguish neighboring pixels' C values). The exact details can be viewed in its open source code. It does this by pushing pixels apart and filling in the gaps. Xaos is a fractal zoomer which caches previously calculated pixels and refines the image when zooming in.
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