HOME | DD

Description
TL : DR on (warning)
This plugin implements the conformal transformation

z' = z + a / z

(Where a is a complex parameter with real and imaginary components)

So yes. It looks like you can get this transform with 1 linear and 1 spherical. Try, it won't work . (And no, you can't use mobius to get this effect)
As simple as it looks, this transformation is not obtainable using the basic plugins but needs a specifically programmed routine because you must enter the inverse function in order to allow Apo to compute it correctly, so it's actually:

z' = z + sqrt( z*z - a )

(I took some math freedom anyway it's basically correct)

This function has the property to be just like spherical near to the origin, similar to julian in a spot of the plane, and finally linear when you get far enough from the origin. There is a smooth transition between those states.

TL : DR off

The plugin has a similar effect to flux (and deltaA), however flux has a pole in (1,0) and one parameter while this has a pole in the origin and two parameters
It's even possible to combine both in a flame, with great effects
See the results in the sample flame pack.

Enjoy! Luca

EDIT 15 10 2018:
Changed the plugin, so it always takes the whole plane to an exact half plane regardless of the transform parameter.
Added an alternate preview parameter by

Description
TL : DR on (warning)
This plugin implements the conformal transformation

z' = z + a / z

(Where a is a complex parameter with real and imaginary components)

So yes. It looks like you can get this transform with 1 linear and 1 spherical. Try, it won't work . (And no, you can't use mobius to get this effect)
As simple as it looks, this transformation is not obtainable using the basic plugins but needs a specifically programmed routine because you must enter the inverse function in order to allow Apo to compute it correctly, so it's actually:

z' = z + sqrt( z*z - a )

(I took some math freedom anyway it's basically correct)

This function has the property to be just like spherical near to the origin, similar to julian in a spot of the plane, and finally linear when you get far enough from the origin. There is a smooth transition between those states.

TL : DR off

The plugin has a similar effect to flux (and deltaA), however flux has a pole in (1,0) and one parameter while this has a pole in the origin and two parameters
It's even possible to combine both in a flame, with great effects
See the results in the sample flame pack.

Enjoy! Luca

EDIT 15 10 2018:
Changed the plugin, so it always takes the whole plane to an exact half plane regardless of the transform parameter.
Added an alternate preview parameter by