What is it ? :
These formulas were inspired by the Orbit Traps colourings and the Barnsley 1 formula. They are based on the equation Z = (z + p)^power + #pixel where p is a parameter depending on where the current z is. It works like an orbit trap.
The Parameters :
Starting point : As in the standard Mandelbrot set, it's the first value of z.
Power : The power of (z + p)
Bailout value : When the fomula decide that a point doesn't belong to the set. If you see strange black regions, decreasing the bailout can help.
Inside mode :
Outside mode :
Inside parameter : The value p takes when it's inside the trap.
On-the-trap parameter : The value p takes when it's on the trap. (Useless when the inside mode and the outside mode are "Raw".)
Outside parameter : The value p takes when it's outside the trap.
Inside spin : This allow you to multiply p by a factor e^(i*Insidespin*d). In the complex plane, p will move along a spiral instead of along a line. Useless if you use the "Raw mode".
Outside spin : Idem Inside spin, but when p is outside the trap.
Flip shape ? : Allow you to flip the shape. (Horizontal lines are mapped into vertical ones and vice versa.)
Mirror shape ? : Allow you to mirror the shape.
Shape offset :
Center of the Shape : Just an advice, if you see a black screen, try changing this parameter.
Shape periodicity : The shape is repeated periodically.
Smoothy periodic ? : Use a smooth repeat function (sin) instead of the usual function.
Concentric Periodicity :
Size of the shape : No comment...
Ratio width/height : ...
Shape parameter :
Graph function : Only with the Graph shape.
Extra graph function : idem graph function
N.B. : To really appreciate the smooth and very smooth modes, use Smoothed Iterations (Mandelbrot) in dmj.ucl or a similar colouring. If the image isn't smooth, try modifying the "exponent" value of the colouring. make also the bailout of the formula and of the colouring match. Idem with the triangle inequality average and cilia coloring.