Explore the Mandelbrot fractal with unlimited zoom using WebGL. Adjust iterations, color maps, and compute Julia sets for any point.
Move through the Mandelbrot parameter plane, zoom into boundary structure, change the iteration limit and color map, or use a selected complex parameter to display its Julia set. The view represents repeated evaluation of a quadratic complex function, with color distinguishing how quickly sampled points escape. The main trap is confusing the two views: a Mandelbrot pixel represents a parameter c, while a Julia pixel represents a starting value z for one fixed c. Higher iteration limits reveal slower escape, but do not add screen resolution.
A concrete input and expected output from the current implementation.
Input
Julia parameter c = 0 + 0i
Expected output
A circular Julia boundary at |z| = 1, with the filled non-escaping region |z| <= 1.
With c = 0, the iteration is z(n+1) = z(n)^2. Magnitudes below 1 approach zero, magnitudes above 1 grow without bound, and magnitudes exactly equal to 1 remain on the unit circle.
Each displayed Mandelbrot location supplies a complex parameter c. Starting from z(0) = 0, the defining recurrence is z(n+1) = z(n)^2 + c. If an iterate's magnitude exceeds 2, that parameter is known to escape. The escape iteration can determine its color; a point that reaches the selected iteration limit without escaping is displayed as non-escaping for that calculation.
In Julia mode, c remains fixed while each pixel supplies a different starting value z(0). Zooming maps the viewport onto a smaller complex-coordinate region. Raising the iteration limit can expose points that escape only after many steps, while changing the color map changes the visual encoding rather than the underlying orbit. WebGL supports updating the fractal as the view and controls change.
No. The Mandelbrot view varies c and always begins its orbit at z = 0. A Julia view fixes one c and varies the starting value z across the image. They use the same quadratic recurrence, but the pixels answer different questions. Choosing another Mandelbrot coordinate therefore produces a different Julia set.
No. A larger cap gives slowly escaping samples more time to escape and can improve classification near the boundary, but the result is still a finite computation on a finite pixel grid. It cannot prove membership for every unresolved sample, and it cannot remove coordinate precision limits encountered at sufficiently deep zoom levels.
The example and behavioral notes were checked against the browser implementation. Standards and primary references below define the relevant format, formula, or platform behavior.
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