There has been a minor update, the Superformula Implementation did not work properly,
i am collecting some formulas to include as example workspaces, check for the latest download 0.61
i know the program lacks documentation, and i need help on that, i will produce some more tutorials
on how to build interesting formulas
here is a "short" description on how to do Orbit Traps Coloring
basically this is done with the new iteration function ITERATECOL,
Short explanaition of the Iteration formula of Mutatorkammer
ITERATE(par1,par2)
Iterate function takes an initialisator for $Z variable ( par1 )
par2 is the formula actually taken for iteration, so for example the mandelbrot formula is
ITERATE(#0,ADD(POW($Z,#2),$PIXEL)))
this should look familar to fractal nerds
ok, then Mutatorkammer has a the possibility to make alternating fractals, this is done
with the ALTERNATE Function
ALTERNATE(par1,par2,par3,[,par4,par5...parN])
par1=initialisator for $Z variable
at each iteration step formula par1,par2 and so on is switched
for example an alternating mandelbrot would be done with the following formula:
ITERATE(#0,ADD(POW($Z,#2),$PIXEL)),ADD(POW($Z,#3),$PIXEL)))
switching a z^2 and a z^3 mandelbrot fractal in each iteration
ok folks, now it is getting more interesting
i come to the conclusion that just offering an iteration function is not enough, so i incporporated
the ITERATECOL function,
ITERATECOL(par1,par2,par3)
par1 is still the initialisator
par2 is a function to evaluate each step, this is known as the coloring methods known in popular fractal programs
the return value for the second parameter is set to the $W variable
par3 is the function wich gets iterated for $Z
ok, and now the method on how to implement orbit traps coloring with these functions
Orbit Trap Coloring with Mutatorkammer
the orbit trap coloring method is based on checking the $Z variable for a lowest distance to a generator function, each iteration step,
Step 1 Take the standard mandelbrot iteration function from above
1 - ITERATE(#0,ADD(POW($Z,#2),$PIXEL)))
Now we need to initialise the $w variable, this is done with the
SETW2(par1,par2)
Function , this function takes a value which will be set to var $W ( par1) and a return value par2
further on we use the ITERATECOL function
2. ITERATECOL(SETW2(#1000,#0),MINABS($Z,$W),ADD(POW($Z,#2),$PIXEL)))
so, what have we done here ? we initialise $w with a big enough value ( 1000 ) initialise the $Z value with #0
the second parameter is the MINABS($Z,$W) part, this is also known as point coloring, making big blobs on the fractal
At last we have to tell that we want to use the $W parameter as colorthis is done with the GETW function, it simply evaluates its
parameter, and returns the current value of variable $W
3. GETW(ITERATECOL(SETW2(#1000,#0),MINABS($Z,$W),ADD(POW($Z,#2),$PIXEL))))
so, now is a good time to save the function in the library, i will now talk on how to further modify the function
the interesting part of the funtion is the MINABS($Z,$W) part, first modification is the center, if we write
MINABS(ADD($Z,0),$W) we simply have the possibility to move the center of the orbit trap, and now we
can incorporate any function build into mutatorkammer to change the trap shape
MINABS(SPIRAL(ADD($Z,0))
would make some nice lines,
the pictures on these pages are done with a trap shape formula like this one
MINABS(SUPER(ADD($Z,0),#1#1,#2#2,#3#3))
the super function is basically an implementation of the Superformula
http://local.wasp.uwa.edu.au/~pbourke/surfaces_curves/supershape/so, the formula wich created these images looked like this:
GETW(ITERATECOL(SETW2(#1000,#0),MINABS(MINABS(SUPER(ADD($Z,0),#1#1,#2#2,#3#3)),$W),ADD(POW($Z,#2),$PIXEL))))
After that the value of $W is mapped to a color with the Voronoi Method, a method to color 2dimensional values, as Complex numbers are!
You can edit formulas in mutatorkammer in the Single Image Tree View, you can drag and drop formula nodes
to anywhere else in the tree, and make new formulas with RIGHT-CLICK!
now i go and include a workspace which contains the above described coloring method!
i will post the update here again!
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