Lambda — Fantastic Fractals

The Lambda fractal is generated from the logistic map, a classic example of how chaotic behavior can arise from a simple non-linear equation. The iteration formula is:

z_{n + 1} = λ z_{n} (1 - z_{n})

This fractal is the Julia set for the quadratic map $f (z) = λ z (1 - z)$ . The parameter $λ$ is a fixed complex number, and the initial value $z_{0}$ is the point on the complex plane being tested.

For more information on the general principles of Julia sets, see the description of the Julia set.

Parameters

GUI Parameters

Iterations: This integer value determines the maximum number of times the formula is applied for each point.

Complex Parameters (Control Points)

Lambda: This is a fixed complex number, $λ$ , that defines the specific shape of the fractal. It can be moved around on the complex plane to explore different variations.