On Gimp-Forum.net denzjos pointed out a very nice page (not only about Gimp):
https://screamingbrainstudios.com/cartesian-transform/

A lot of examples and explanations including:
G'MIC-Qt / Deformations / Cartesian Transform



A bit out of date because the formulas will not work if they contain the letter a - but it will be enough to change it to another one (after the update in 2023 A, B, C, D are reserved for constants).

I am fascinated by the power of this filter.











Maybe someone knows other pages on this topic?

It is also an inexhaustible possibility of creating animations.
Animation examples reduced to the limitations of attachments.





How to easily write plugins to create animations from G'mic (a few lines of code), you can see in Animation_cartesian_transform.py

Rotating Ball



Type: Circle Transform



Type: Spherize

MareroQ, Thanks a lot for your plug-ins.

Thank you so much Isabella for playing with me

It's really funny, MareroQ. Thank you so much.

I want to learn too.

, ask if you need some help.

Am I missing something?

Don't be discouraged because you are on the right track.
It's just that after obtaining the layers (let's say 10 layers) you leave layer 10 as it is and now you reverse the layers to get the opposite effect.
Layer 10 as it is, layer 9 you duplicate it and place it on top of layer 10, which will be layer 11. Layer 8 you duplicate it and place it on top of layer 11, which will be layer 12...and so on until the original image layer.
You give the top layer a pause of (1000ms) so as not to overwhelm the effect.
It's that easy.
Good luck, DJ

Making a Ping-Pong effect is time-consuming - there are various plugins for it.
I'm posting the simplest version here (without GUI).
In the menu:



XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX

Spiral Riple



The Radial Slice preset lets you create two types of seamless images:
1. Relative Warping
Source:


Result:


2. Radial
Source:


Result:


These new interesting possibilities of creating seamless textures and many types of deformations have been added to MrQ Pattern Editor Ver.11Ver.11.

Hi MareroQ, thanks for your new filter.
It seems that I can't enjoy it because I don't have version 3.5 installed
Even though I have installed it, it's not visible in the layers list.
My Gmic version is 3.3.5
Thanks anyway.

Hi Issabella

I didn't understand which filter doesn't appear in the menu?
Registration in the menu itself doesn't depend on the G'MIC version.
All animation filters listed here have a location:
Filters ➤ Animations ➤ Cartesian Transform 'Name'...
The Ping Pong plugin is located in the Layers context menu (right mouse button).

Thank you so much MareroQ.
My problem is that having the filter installed, I can't see it. it doesn't show in the list.
I don't know the reason.
Please, see the shots.

OK.
I wasn't specific enough in the description.
You need to click on the layer in the Layers dock.



Notice the difference between Layer and Layers.
Just in case, I'm including the version that registers in the menu:
Filters➤Animation➤Ping-Pong Layers for Animation
(You can keep both versions).

Just, It was that.
Happy with the result and a helpful filter, MareroQ.
Thank you so much

Just I have installed your other filter to keep both. Thank you so much.