a day ago
- The Mandelbrot Set consists of complex numbers that remain bounded under repeated iteration of the equation z_{n+1} = z_n^2 + c.
- The algorithm iterates until the magnitude of z exceeds 2 (radius-2 circle) or reaches a maximum iteration count, then colors pixels based on escape time.
- Complex numbers have a real and imaginary part, plotted on the complex plane with real on x-axis and imaginary on y-axis.
- A common technique in the Mandelbrot generator is remapping number ranges, e.g., converting pixel coordinates to complex plane coordinates or escape counts to colors.
- The pseudocode demonstrates the core loop: for each pixel, compute c from screen coordinates, iterate z until it breaks radius 2 or max count, then color accordingly.
- The article also covers practical implementation details like Adam7 interlacing, cooperative multitasking in JavaScript, and floating-point resolution limits.