One of my favorite Youtube Channels is Numberphile. They are one of the driving forces behind my newfound interest in maths. In a recent video they shed some light onto a sequence of numbers called Recamán’s Sequence.

The amazing part here was the visualization that they developed for Recamán’s sequence: A beautiful pattern of semicircles that result from tracing the sequence’s jumps on a number line.

In this tutorial we’ll generate Recamán’s sequence and then visualize it using VEX only.

WOW Moritz , fantastic work you left me stunned, awesome, it is very nice to have you supporting us with your absolute control of VEX and everything else of Houdini.

https://vimeo.com/278066865

Moritz, this is both elegant and potent in it capacity to generate a beautiful visualisation of the Recamán Sequence. Thank you for your lucid explanation.

Do you think it is possible to extend the method by generating points in n-dimensional space?

Starting with 4-D, one could conceivably navigate throughout neighbouring regions of such a space and visualise this journey by generating 3-D cross-sections.

Perhaps though the probability of revisiting a point may become too small in which case one could define a region instead.