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Home/Math Visualization/Julia Set Explorer

Julia Set Explorer

This interactive simulator explores Julia Set Explorer in Math Visualization. Pick c by clicking the embedded mini-Mandelbrot or animate c along a circle; Fatou dust vs connected sets. 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

  • julia
  • set
  • explorer
  • julia set
  • math
  • visualization

Parameters c = Re + Im·i

-0.7
0.27015
180

Gallery

Measured values

Re(c)-0.70000
Im(c)0.27015
|c|0.7503
c inside M?—
max iter180

How it works

Julia set for a fixed parameter c: pixels are colored by how fast the orbit zₙ₊₁ = zₙ² + c escapes for that z₀. Picking c inside the Mandelbrot set gives a connected fractal; picking c outside gives a Cantor dust of disconnected points. Click on the small Mandelbrot map to pick c, or hit ▶ to walk c around the circle of radius 0.7885 — the Julia set morphs in real time.

Key equations

J(c) = ∂{ z₀ ∈ ℂ : supₙ|zₙ| < ∞ }, zₙ₊₁ = zₙ² + c
connected ⇔ c ∈ M (Fatou–Julia)