How much computation can you fit in a voxel?

How much computation can you fit in a voxel?

If circuits were designed to take advantage of three dimensional space, how much information could they process per unit of space occupied? We will assume that our unit of computation is one indivisible unit, or in this case a voxel.

First let’s think about input/output. There are six faces to a three dimensional cube. So this gives us a total of six exterior faces. Let’s assume that their is some internal face, giving us a total of seven. Then let’s assume that each face can process both input and output.

Second, what can connect and transfer information? Let’s assume that voxels, like the long winding neural paths in our brains, can match an input with output face, or vice-versa. This also means that multiple outputs can be joined to a single input. Let’s assume that all joined output is additive in signal strength.

Third, how do signals transfer? From animal brains we can see that there is some electrical activity that we would like to replicate here. So, each input face has a low and high state and a range of values in between.

Finally, how do we create a logical circuit out of a voxel? Well, in the most general form, we can create a function to map from input to output. In other words, one voxel is a pure function mapping seven dimensional input to output. It follow then that we can do things like concatenate whole voxels to other functions. Here we derive a bunch of math that is normally associated with computational intelligence. The degenerative cases can easily handle lower dimensional logic and gates; this turns out to be a quite powerful mode of computation.

So, in summary, voxels are pretty powerful units of computation. A voxel brain should be pretty powerful; and we are going to test this.