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Home/Math Visualization/Mandelbrot Deep Zoom

Mandelbrot Deep Zoom

This interactive simulator explores Mandelbrot Deep Zoom in Math Visualization. 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.

Who it's for: For learners comfortable with heavier math or second-level detail. Typical context: Math Visualization.

Key terms

  • mandelbrot
  • deep
  • zoom
  • mandelbrot zoom
  • math
  • visualization

Parameters

220

Famous spots

Shortcuts

  • •Drag to pan
  • •Mouse wheel to zoom (under cursor)
  • •R — reset view

Measured values

center Re-5.0000e-1
center Im0.0000e+0
view span2.600e+0
zoom factor1.00e+0×
max iterations220

How it works

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.

Key equations

zₙ₊₁ = zₙ² + c, z₀ = 0
M = { c ∈ ℂ : supₙ |zₙ| < ∞ }
μ = n + 1 − log₂ log₂ |zₙ| (smooth iter)