Leaf 3

[element90]

A fractal from the last days of Mars before work started on its replacement (Saturn). The formula used here is:

Formula: Luzcpac

z <- log(unsign(z^alpha) + c)

This formula became Ltzcpac in Saturn in a more flexible form:

z <- log(transform(z^alpha) + c)

To get the same results as Luzcpac the transform function is set to "top right" which in its default form removes the sign from both the real and imaginary components of z. The reason it is called top right is that the values are "folded" into the top right quadrant of the complex plane, the position of the origin can also be moved and the plane rotated as part of the transformation.

A note of naming fractal types: for Mars Luzcpac, "L" for log, "u" for unsigned, "zcp" for z to a complex power and "ac" for add constant, for Saturn "t" for transform replaces "u". A number of formulae in Saturn appear in 4 forms, i.e. four forms of the basic formula, in this case the basic formula is:

z <- z^alpha + c

and it comes in four forms, Zcpac, Lcpac, Tzcpac and Ltzcpac:

z <- transform(z)
z <- z^alpha + c

z <- transform(z)
z <- log(z^alpha) + c

z <- transform(z^2) + c

z <- log(transform(z^2)) + c

The default transform is "no-op" or "identity" i.e. does nothing.
 
Where a "t" appears in a name it means that the transform is applied in the formula otherwise it is applied before evaluating the formula. This lose naming convention is used for some of the simpler fractal types in Saturn but it becomes difficult to apply as the formulae get more complicated. The fractal names used in Saturn will be unfamiliar as they rarely match names used in other programs, also by employing transforms several well known fractals can be produced using one fractal type in Saturn.

The parameters in text form can be found on the deviant art page for the fractal: http://fav.me/d3iq2ad