If some z_k does, the sequence "goes to infinity" otherwise, you can consider it as bounded. In practice you can check, while iterating, if the absolute value of one of the 20 terms is greater than 2 (if one of the terms does, the subsequent terms are guaranteed to be unbounded). For each point/pixel, let C be that point, compute, say, 20 terms of the corresponding iterated sequence z 1, z 2, z 3.Cover the rectangle with a suitable rectangular grid of points (say, 400x400 points), which will be mapped to pixels on your monitor.Choose a rectangle in the complex plane (say, from point -2-2i to point 2+2i).In practice, to draw the Mandelbrot set you should: it does not go to infinity, is the Mandelbrot set (the black set in the figure on the Wikipedia page). The set of those constants C for which the sequence z 1, z 2, z 3. you compute z 1 = f(0), z 2 = f(z 1), z 3 = f(z 2) and so on. Now you iterate it starting from z = 0, i.e.
Where z is a complex variable and C is a complex constant. You start with a function of complex variable You should indeed start with the Mandelbrot set, and understand what it really is.
#Ultra fractal flowers how to#
Screen.Plot(x,y, iterations % maxColors) //depending on the number of iterations, color a pixel.ġ.) Learn exactly what the Square of a Complex number is and how to calculate it.Ģ.) Figure out how to translate the (-2,2) rectangular region to screen coordinates. While(Complex.Abs(Z) < 2 & iterations < maxIterations) Int maxColors = 256 // Change as appropriate for your display. Int maxIterations = 10 // increasing this will give you a more detailed fractal public void MBrot()įloat epsilon = 0.0001 // The step size across the X and Y axis When done, color the original pixel depending on the number of iterations you've done.
If the distance from the origin is greater than 2, you're done. If you reach the Maximum number of iterations, you're done. = ^2 + while keeping track of two things:Ģ.) the distance of from the origin. So, start by scanning every point in that rectangular area.Įach point represents a Complex number (x + yi). The Mandelbrot-set lies in the Complex-grid completely within a circle with radius 2.
#Ultra fractal flowers code#
Version 4 added support for animations and improved flame fractal rendering.įormulae from Fractint, an early and widely used piece of fractal-generating software, have been converted to an UltraFractal formula file.My quick-n-dirty code is below (not guaranteed to be bug-free, but a good outline). Other features include fullscreen mode, color cycling, a render queue, distributed rendering calculations, and a detailed help file.
#Ultra fractal flowers software#
The software calculates statistics about the fractal that is being previewed. The GUI is customizable with a dockable MDI. Ĭalculation using arbitrary precision arithmetic is supported, allowing users to zoom to a magnification of 10 4000. There is a busy mailing list on which many users post their parameter sets. Fractals may be copied from the interface and pasted as plain text into an email. Fractal formulas, coloring algorithms, and transformations may be written by users, and a large number of such formula files are available in a public formula database. The program works using a similar paradigm to Photoshop, allowing multiple layers to be combined using layer blending modes, transformations, and custom fractal formulas.
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