Fractal Generator

This interactive simulator explores Fractal Generator in Math Visualization. Mandelbrot, Julia, Koch snowflake. Zoom infinitely. 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

  • fractal
  • generator
  • fractal generator
  • math
  • visualization

How it works

Explore **Mandelbrot** and **Julia** sets via escape-time iteration **z ← z² + c** (Mandelbrot: start at **z = 0** and vary **c**; Julia: fix **c** and vary **zā‚€**). **Pan** with the mouse, **zoom** with the wheel. **Koch snowflake** is a classic self-similar curve built by replacing each segment.

Key equations

Mandelbrot: zā‚€ = 0, Ā  zā‚™ā‚Šā‚ = zₙ² + c Ā  (c scans the plane)
Julia: c fixed, Ā  zā‚€ = pixel, Ā  zā‚™ā‚Šā‚ = zₙ² + c