Lucky script by EA seems to be monster. Kind of a way to hybridise all of kaliset / ducks/ ducky / talis / whatever pattern generating formulas.
Lucky, a Ducky special
I. Lucky as such
Lucky doesn't use new formulas, it uses existing codes, with some small
variations in the way the iterations are carried out. They often give
interesting symmetrical patterns. Although there are many self-similarities,
I don't think all these results are fractals in a math sense, some are,
others not or are doubtful.
First of all some definition. When I speak of a 'formula', I mean a maths
formula, without conditional requirements. If conditions are present,
I speak of a 'script' or 'code'. So UF consists of mapping, fractal and
coloring scripts. The math formula only has standard functions and parameters.
Lucky is a subset of Ducky (the latter has been baptized in such way by
Elias Rain). The well known mushroom/parachute pattern of Ducky is not its
main characteristic. The real one is the interrupted orbit. Every time
the argument of the points of an orbit exceeds the limit of 90 degrees
(p/2 radians) it will be put back by the abs function. In graphics it
means that it will be mirrored in relation to the vertical axis (where
Im(z) = 0), so that it will be thrown back into the first quadrant. Thus
it becomes clear that the 'natural' spiral structure will be disturbed and
that the resulting shape of orbit points soon will be very difficult.
The specialty of a Lucky is that some iterations will follow a different
pathway. We restrict ourselves to two possible pathways, each with
different parameters or even with different basic functions.
The Lucky script has been split into two parts: a first and a second code.
In the default mode ('series'), 'first-second separated' unselected,
every iteration will follow either path 1 or path 2, depending on parameters
'main condition'.
The following examples (with the option 'variant' off) may clarify how
it works:
....
Not a shure if I should share authors message from a Ultra Fractal mailing list. But this one looks as ultimate pattern formula.