Math is incredible. There is a branch of it called Spherical Geometry and a couple other pieces that all come together and help us “unwrap” a sphere into a flat surface.
There is lots of ways to do it too! And if you repeat patterns, some very cool things happen that start to look like fractals!
Take a look at the photos for a samples above, and check out the instructions below (instructions thanks to Carl Bennett!).
These things are fun. Here’s how to install and use the necessary software:
Download and install GIMP from here: http://www.gimp.org/
Start GIMP, wait for it to open and then close it. This will initialise a folder that MathMap needs to use
Download and install MathMap from here: http://www.complang.tuwien.ac.at/schani/mathmap/
Hold down the windows key on your keyboard and push r to bring up the Run dialog.
type %userprofile% and push enter.
You will see a folder named .gimp-2.6 and one named .gimp-2.8
cut and paste all the files inside .gimp-2.6 into .gimp-2.8
download this file http://pastebin.com/9ZjLwPn7 Rename it to Quincuncial.mm
and save it to the subfolder encountered earlier: .gimp-2.8\mathmap\expressions
Now open your Theta pic in GIMP and go to the menu item Filters->Generic->MathMap->MathMap
Go to the Filters tab and select Quincuncial and push the preview button
Then go to the User Values tab to find the settings. You should not need to change ImageH but all the others are described in Quincuncial.mm which can be accessed from the Expression tab
Play with the sliders at leisure.
Push OK when you’re done.
Bonus optional steps:
Extract the files in this zip to the same expressions folder http://www.lightspacewater.net/…/Mathmap/equirectangular.zip
Open your pic and go to MathMap, as before.
On the Filters page select Equirectangular\erect_rot
Push Preview and change to the User Values tab to straighten/distort your image
Now go to the Composer tab
click on erect_rot and Quincuncial and arrange the boxes so you can see them both
Drag the little circle in erect_rot’s OUT to Quincuncial’s IN and a red line should join them. And push Preview
now when you’re in the User Values tab you’ll have three extra sliders to turn the elements in your image
Carl’s Example Photo: