Mandelbrot Set

You've probably heard of the Mandelbrot set, but what is it? It's a fractal demonstrating beauty in mathematics, and it demonstrates how a simple algorithm can result in an extremely complex and intricate design.

How does the Mandelbrot set work? You start with the coordinates of a pixel within the Mandelbrot set. Those numbers are changed repeatedly according to certain formulae. There are two possible results of this process that are of concern in the Mandelbrot set: either the numbers remain small and dance around 0, or they become large and fly away. If the numbers ever leave the vicinity of zero, the pixel is lit, otherwise it's black. The black areas of the Mandelbrot set are normally slower to display because those pixels must go through the most iterations to determine whether they will go out of bounds. The number of iterations that are required to make the coordinates leave the area usually determines the coloration of the lit pixels, often resulting in beautiful patterns of colors.

Providing a more accurate picture of the Mandelbrot set often requires more iterations. Only a few hundred iterations may be required with each pixel to show the Mandelbrot set at the lowest zoom level, but as you zoom in, more iterations are required per pixel to provide an accurate picture without artifacts that could change from one rendering to the next. You could literally zoom in forever in the actual Mandelbrot set, but most computerized reproductions have limited precision of numbers and math operations, meaning you can only zoom in so far. However, the number of locations to explore is still almost infinite to the human mind. You could spend the rest of your life exploring the Mandelbrot set and still find new places that no one has ever seen.

The Mandelbrot set never changes, so if you find an interesting place, you can save the coordinates and zoom level to go back there later.

Below ↓ and to the right → are some free Mandelbrot desktop background / wallpaper pictures.

Mandelbrot set fractal desktop background wallpaper 1 Mandelbrot set fractal desktop background wallpaper 2 Mandelbrot set fractal desktop background wallpaper 3

Try my free online Mandelbrot Explorer software. It was coded in JavaScript and was used to make the above images.

Mandelbrot Explorer

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©2019 Ron Spain

Mandelbrot set fractal wallpaper Mandelbrot set fractal background Mandelbrot set fractal desktop background