Tick Tock*

2D projections of advancing 6-simplex inflation

By t+7, Tick Tock inflation of the 6 simplex produces over a million nodes, 1,055,180 to be precise, which we can map onto a 7 dimensional coordinate space where each coordinate can range from zero to 729. The dimensions are all equivalent so we can choose any 2 to be x and y and form 2D projections of the positions of the node in 7D space, with the colour of each corresponding pixel representing some measure of the 7D points which project onto that position.

One of the first obvious features of such a projection is that there are many regions of the x, y plane which are devoid of any nodes. The coordinate system used means even after 2 dimensions are chosen, the other 5 are still equivalent. In all the 2D projection GIFs shown, (0, 0) is in the upper left corner, so they are symmetric about the NW-SE diagonal.

Density plot of projection from 7D to 2D of 6-simplex at t+7

Minimum z plot on projection from 7D to 2D of 6-simplex at t+7