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.. _sffe:
.. _usrform:
.. _usrformInit:
.. index::
pair: menu item; User formula
pair: menu item; User initialization
pair: command; usrform
pair: command line option; usrform
pair: command; usrformInit
pair: command line option; usrformInit
single: sffe
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:
z
current sequance point Z(n)
c
current plane 'point'
p
previous sequence point Z(n-1)
Constants
---------
Format for complex numbers is **{re;im}** eg. {3;2} is complex number 3+2i.
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) - 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
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