I am thinking about 1D grid cell modules and how to best design rules to code it. I think 1D modules are right way to go, instead of 2D, because it is more general and could allow to have n-dimensional space, with for example one of basis vector representing twist motion forward etc… like jeff mentioned in one of the meetings.
What do you think about following:
Consider three grid cell modules:
GCM1 : [0 0 1]
GCM2 : [0 1 0 0 0]
GCM3 : [0 0 0 1 0 0 0 0]
Sizes are 3,5,8.
The three modules represent uniquely one position in 1D space that is 120 in size (it is least common multiple of the individual sizes).
For first position in space it is:
1 0 0
1 0 0 0 0
1 0 0 0 0 0 0 0
For moving in space just shift to the right by the distance. Rolling over.
1 0 0
0 0 0 1 0
0 0 0 1 0 0 0 0
If you move by distance 3.
If you want to get distance between two positions, just start at first and keep shifting till it match. Number of steps you’ve done is equal to the distance.
If you would have more of these three packs, you could represent more dimensions. If you want to move in that space, you will update them individually depending on the direction that you want to move.
About scales: scale is just mapping of the internal representation to the real world, e.g. how much move your muscles etc.
Also unions would work same as with 2D Gcms, if you have large enough space, then chance of false positives are surpressed at low level.
Are there any flaws of this thinking?