# 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