fractals: Mandelbrot escape function

In shabbychef/faroutman: Shiny Fractal Viewer

Mandelbrot escape function

Description

Compute the Mandelbrot set.

Compute the Fibonacci set.

Compute the Cosine set.

Compute the Exp set.

Compute the Burning Ship fractal set.

Usage

mandelbrot_esc(x, y, maxit = 128L, escape = 4)

fibonacci_esc(x, y, maxit = 128L, escape = 4)

cosine_esc(x, y, maxit = 128L, escape = 987)

exp_esc(x, y, maxit = 128L, escape = 2500)

burning_ship_esc(x, y, maxit = 128L, escape = 4)

Arguments

x	the real coordinates
y	the imaginary coordinates
maxit	the maximum iterations to consider
escape	the condition to determine escape, in squared distance units.

Details

Computes the iterations required to escape based on z_n \leftarrow z_{n-1}^2 + c given input c.

Computes the iterations required to escape based on z_n \leftarrow z_{n-1}^2 + z_{n-2} + c given input c.

Computes the iterations required to escape based on z_n \leftarrow cos(z_{n-1}) + c given input c.

Computes the iterations required to escape based on z_n \leftarrow exp(z_{n-1}) + c given input c.

Computes the iterations required to escape based on z_n \leftarrow \left(|Re(z_{n-1})| + i |Im(z_{n-1})|\right)^2 + c given input c.

Author(s)

Steven E. Pav [e-mail]

References

Wikipedia contributors, "Burning Ship fractal," Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/w/index.php?title=Burning_Ship_fractal&oldid=1145232996 (accessed March 27, 2023).

See Also

https://math.stackexchange.com/a/5705

shabbychef/faroutman documentation built on March 28, 2023, 10:42 p.m.