For faster drawing: https://turbowarp.org/1321269863 Watch the Mandelbrot set appear before your very eyes! When drawing finishes, adjust the values and press anywhere to zoom in. Press the magnifying glass with a minus sign to zoom out. Press the circular arrow to redraw. If the drawing takes too long, press the stop button.
The Mandelbrot set is a famous fractal, produced by the equation z_(n + 1) = (z_n)^2 + c in the complex plane, where - z_n is a complex number (a + bi) starting at 0 - i is the imaginary unit, equal to the square root of -1 - c is another complex number, given by the coordinates x + yi (stays constant) - z_(n + 1) is the result of the calculation. This is repeated a certain number of times with z_(n + 1) as the new z_n. If a^2 + b^2 exceeds 4, the result heads to infinity and calculation stops, with the point colored based on how fast it took off. Otherwise, the point is part of the Mandelbrot set, shown in purple. Zooming into fractals reveals nearly identical copies of themselves. This makes them self-similar, and they appear in nature (trees, snowflakes, broccoli, clouds, rivers, shorelines, lungs, galaxies, lightning, etc.). NOTE: The graphics become blocky at very high zoom levels due to technical limitations. Thumbnail image: https://en.wikipedia.org/wiki/File:Mandel_zoom_00_mandelbrot_set.jpg Music: - codbarley: Distant Sky - Eschatos: Point of No Return (Super Mario World port) - Kevin MacLeod: The Builder (incompetech.com, CC BY 4.0, https://creativecommons.org/licenses/by/4.0 ) - @KnightKit12: Elevation - Little Alchemy 2: Statistical Self-Similarity - Mikael Manvelyan: New Game - Nekoprism: Dreaming Together - Nintendo 64DD startup (intro) - @PaulRHJT: Home Sweet Home - Vexento: Pixel Party - VVVVVV: Passion For Exploring - @Xaf: Unlimited #fractal
