XaoS online help - Using user formulas
Description: XaoS, realtime, fractal, zoomer

# Using user formulas

XaoS supports entering your own custom formulas. Select `User formula` from the `Fractal` menu to define a custom fractal formula. Select `User initialization` to change the sequence starting point z0. By default z0 is set to 0. User formulas should be interpreted as functions in the form
Z(n+1) = formula (Z(n), Z(n-1), C).

In user formulas, as shown above, three variables are available:

z
  current sequance point Z(n)
c
  current plane 'point'
p
  previous sequence point Z(n-1)

Format for complex numbers is {re;im}
eg. {3;2} is complex number 3+2i.

Available functions are listed below:

basic operations
  +, -, *, /

basic trigonometry
  sin, cos, tan, cot
  asin, acos, atan, acot
  sinh, cosh, tanh, coth

Exponential and logarithmic functions
  exp
  log - natural logarithm
  log2, log10
  logN (base, z) - logarithm of base N (where N is integer)
  logCN (base, z) - logarithm of base CN (where CN is complex)

power functions
  powi - power with integer exponent (fastest)
  powd - power with real exponent
  powdc - power with complex exponent
  pow - same as powd
  sqr - square

square functions
  sqrt - square root of a complex number
  rtni (z, n, i) - i-th root of n-th orgder

other functions
  rand (max) - random real number in range [0, max)
  inv - inverse
  abs - absolute value
  re - real part
  im - imaginary part