Fractal Generator V.1 #all #art

Instructions

Welcome To: ==============Fractal Generator============= Try https://turbowarp.org/1298870136 for absolutely zero lag. I highly recommend TL; DR: Pen settings for colour. Some nice Julia sets have parameters -0.8+0.156i or 0.4 + 0.4i is nice. If you want different ones, you can ask chat gpt or something. Notes: on some devices, there may be some visual glitches, for example, in mobile, the color spectrum is too big for its border. How to Use it: Click start now to choose a fractal to generate or click pen settings to choose your desired colour. Some Julia sets you may not see as well, or you may think of them as "lame." This is because when your parameter is not in the Mandelbrot set, the points in your Julia sets are very disconnected. These are known as Cantor dust. If you are confused as why your Multibrot Set looks like a Mandelbrot set is because it is. A Multibrot set at d = 2 is literally a Mandelbrot set by definition. Information: In Fractal generator, there are 4 different types of fractals that appear in complex dynamics: Mandelbrot Set: The Mandelbrot Set is the set of all points C on the complex plane such that if you infinitely iterate a certain function starting from 0, the number stays bounded and doesn't blow off to infinity. The function is defined as an iterated function Zₙ₊₁ = Zₙ²+c. Discovered by Benoit Mandelbrot Julia Set: Unlike the Mandelbrot Set there are many different types of Julia sets. The iterated function is similar to the function that defines the Mandelbrot set but with a fixed constant C and the Julia set are all the values of Z such that it stays bounded when put through the iterated function. If the value C of the Julia set C is not a part of the Mandelbrot set, the fractal can look very disconnected and dispersed. These sets can b e known as Cantor Dust. Discovered by Gaston Julia. The Burning Ship Set: The Burning ship set is a slight variation of the Mandelbrot Set, defined by the set of all values C such that when the iterated function: (|Re(zₙ)| + |Im(zₙ)|i)² = zₙ₊₁ where Re(z) is the real part of z and Im(z) is - as you would expect - the imaginary part of z. Discovered by Michael Michelitsch and Otto E. Rössler. Multibrot Set: The Multibrot sets are variations of the Mandelbrot set where instead of squaring Z and adding a constant, you raise Z to a higher power such as 4 or so. The exponent is usually represented as the letter d and for a Multibrot set at d, the image somewhat resembles a d-1-gon (a polygon with d-1 sides.) Also discovered by Benoit Mandelbrot. If you read everything up till here, I thank you because this took me a while to write. If you didn't read it but u scrolled down to here, then idk lol.