RUN IN TURBO MODE (shift-click the green flag) Enter the pen thickness (recommended: 3) Enter the fractal type (mandelbrot or julia) Enter the function type (normal, cubic, or conjugate) Enter the parameters (for mandelbrot, set both to 0 for normal mandelbrot. for julia, enter the parameters) Press z to zoom in on an area. Press o to zoom out. Press space to see the coordinates. Press j on the mandelbrot set to see the julia set. Press t to set thickness.
The set at the beginning is pre-rendered. It was generated with thickness 1. Thickness 1 makes the best images, but takes a long time. I made it randomly generate pixels so you can see a rough idea of the set before you get a precise picture. If you do not put a correct type in the fractal or function, it defaults to mandelbrot and to normal. TECHNICAL STUFF: The mandelbrot set is a fractal on the complex plane. The complex plane is made of complex numbers (If you don't know what those are, see https://scratch.mit.edu/projects/273447413/). To see if a complex number is in the mandelbrot set, start with zero. then repeatedly square the number and add a given constant. If its distance from zero stays within 2, it is in the mandelbrot set. If it escapes outside of 2 and goes to infinity, it is not. The black points are the points that are inside the mandelbrot set; the points outside the set are colored based on how long it took to escape. The mandelbrot set is a fractal, meaning no matter how close you zoom in, it still looks rough. like many fractals, it has self-similarity, meaning it contains smaller versions of parts of itself inside itself. The circle on the end of the largest circle is identical to the largest circle, and there are smaller mandelbrot sets inside the mandelbrot set. There is also a similar kind of fractal called a julia set. A julia set has a given constant, and to determine whether a number is in a julia set, you take the number and repeat squaring it and adding the given constant. If a number is in the mandelbrot set, its julia set is connected, if it is not, the julia set is not connected. The mandelbrot set could be seen as a map of all julia sets. But what if you started at a different number on the mandelbrot set? You get a distorted version of the mandelbrot set. I first saw this type of fractal in a video. The julia sets could be thought of as forming a 4D fractal, which the mandelbrot set is a 2D slice of. Besides the mandelbrot and julia sets, there are 4 other ways to slice this fractal. You can see them by doing rR, rI, iR, or iI. Some are more interesting than others. In addition, there are function types. Normal is the normal one. Cubic cubes instead of squares, giving a more symmetric fractal. Conjugate inverts the imaginary part to produce the strange skewed mandelbar. Absolute takes the absolute value of both sides before squaring to generate the bizarre "burning ship" fractal. But you don't need to understand all that math to see some fascinating patterns.
