Euclidean rhythms are a type of rhythm found in many musical styles. To make a Euclidean rhythm, break up a time interval into equal-length steps. Then place a beat at the beginning of some of the steps. If the beats are as evenly-spaced as possible, the pattern is a Euclidean Rhythm.
For example, you can make a rhythm with 2 beats on 4 steps. It will be Euclidean if the beats are on step 1 and 3 (or on step 2 and step 4).
Here’s a more interesting example: 5 beats on 16 steps. To distribute the beats as evenly as possible, you must put them on steps 1, 4, 7, 10 and 13 (or the same rhythm shifted in time). When shifted by 6 steps this is the Bossa Nova rhythm.
The MIDI Output Type is used to trigger sounds created outside of Euclidium, either by other apps or by external hardware like synthesizers. Additional software or hardware may be required.
On macOS, you first need to enable the virtual midi port using Audio MIDI Setup. See https://support.apple.com/guide/audio-midi-setup/transfer-midi-information-between-apps-ams1013/mac
On iOS, unfortunately Garage Band doesn’t easily support virtual MIDI instruments, so we haven’t found a way to integrate Garage Band and Euclidium. (If you know how to do so, please let us know!)