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