Newton Fractal
This interactive simulator explores Newton Fractal in Math Visualization. Basins of attraction for Newton iteration on zⁿ−1 with adjustable relaxation ω. 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
- newton
- fractal
- newton fractal
- math
- visualization
How it works
**Newton’s method** for **p(z) = zⁿ − 1** colours each starting point by **which root** the iteration **zₙ₊₁ = zₙ − ω·p(zₙ)/p′(zₙ)** converges to. The boundary between the **basins of attraction** is a **fractal** with the property that **near any point of three different colours all three colours meet** — Newton himself never imagined this. Try **n = 4 or 5** for the most photogenic basins; **ω ≠ 1** turns it into a **relaxed** scheme with very different boundary structure.
Key equations
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