User formula

User formula hint

Thanks to the user formula, GNU Xaos allows you to create a rendering or a structure at will. With this command you can find a more innovative fractal structures than traditional chaotic structures.

How is a fractal formula structured?

A fractal formula is structured so:

  • z: current sequence point
  • c: current plane point
  • p: previous sequence point
  • i: imaginary unit

The iterative functions, however, are structured so:

  • Simple iterative functions: z0 = f(z) + c
  • Iterative functions that use c as variable: z0 = f(z, c)
  • Complex functions: z0 = f[g(z, c)]+c
  • Specific functions that use multiple variables: z0 = f(z, p, c)

Function library

Arithmetic operators +, -, *, /, ^

Trigonometric functions:

  • Simple trigonometry: sin, cos, tan, cot
  • Inverse trigonometry: asin, acos, atan, acot
  • Hyperbolic trigonometry: sinh, cosh, tanh, coth

Exponential and logarithmic functions:

  • Exponential function with base 10: exp
  • Natural logarithm: log
  • Logarithms base 2 and 10: log2, log10
  • Logarithm base n: logN(n:I; z:C) (note: I=Integer, R=Real and C=Complex)
  • Complex logarithm base n: logCN(n:C; z:C)
  • Exponentially with integer exponent n: powi(z:C; n:I)
  • Exponentially with real exponent n: pow(z:C; n:R) or powd(z:C; n:R)
  • Exponential with complex exponent n: powdc(z:C; n:C)
  • Square of z: sqr
  • The inverse of a complex number z: inv
  • Square root: sqrt
  • i-th root of n order: rtni(z:C; n:I; i:I)

Other functions:

  • Random function with range [1; m[: rand(m)
  • Real absolute value: rabs
  • Complex absolute value: abs
  • Real part: re
  • Imaginary part: im

Practical Examples

  • Mandelbrot's burning ship function: sqr(abs(re(z))+i*abs(im(z)))+c
  • Mandebrot fractal with n-th order: z^n c
  • Special function: ((z^3*(p^-2 1))-1)*0.45+c

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