Mandelbrot Deep Zoom
This interactive simulator explores Mandelbrot Deep Zoom in Визуализация математики. Drag/wheel deep zoom into the Mandelbrot set with smooth continuous coloring and named landmarks. Use the controls to change the scenario; watch the visualization and any graphs or readouts to connect the model with lectures, labs, and homework.
Для кого: For learners comfortable with heavier math or second-level detail. Typical context: Визуализация математики.
Ключевые понятия
- mandelbrot
- deep
- zoom
- mandelbrot zoom
- math
Как это работает
**Mandelbrot set** is the set of complex **c** for which the orbit z₀=0, **zₙ₊₁ = zₙ² + c** stays bounded. Each pixel is coloured by how fast it escapes (the **escape-time algorithm**). With **continuous** smoothing μ = n + 1 − log(log |z|)/log 2 the bands disappear and you can dive into self-similar valleys — try **Seahorse Valley** or the **mini-Mandelbrot** preset and crank up *max iterations* before the colour goes flat.
Основные формулы
Ещё из «Визуализация математики»
Другие симуляторы в этой категории — или все 42.
Julia Set Explorer
Pick c by clicking the embedded mini-Mandelbrot or animate c along a circle; Fatou dust vs connected sets.
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L-Systems (Turtle)
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Bézier & de Casteljau
Drag control points; live recursive linear-interpolation scaffolding evaluates B(t).
Delaunay & Voronoi
Bowyer–Watson triangulation and dual Voronoi tessellation; click to add seeds, drag to move.