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).

Variables

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

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

Constants

Format for complex numbers is {re;im}, e.g. {3;2} is complex number 3+2i. You must write constants for the coordinates. If you need to express a complex number with a non-constant, split it to real and imaginary parts like this: (re(z)+im(z)*{0;1})^2+c.

Functions

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) - ith root of nth order

other functions

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

Notes

• The entered formula will always be rewritten in capitalized letters.