See https://www.youtube.com/watch?v=094y1Z2wpJg.

This is about sequences having just these rules:

• if value y is even, then divide it by 2
• if it's odd, then turn it into `3*y + 1
• extra rule: if y is equal to 1, interrupt the sequence (it would otherwise get into a 4-2-1 endless loop),

and keeping track of the "tallest" and "widest" sequence obtained so far (progressively increasing the initial value).

Plot images of such sequences go into plots/*/. For example:

• A recent Python 3.
• Matplotlib.

python x3p1.py

You can stop execution with CTRL+C. You can resume later, and computation will start from where you left. If you want to start everything over, delete the file .cache.json.

See https://www.youtube.com/watch?v=TzE3z4Burdk.

Video was made with

ffmpeg -framerate 2 -pattern_type glob -i 'plots/jpg/*.jpg' out.mp4