Maybe I am seeing your problem. The 100 or so cells that make up a mini-column compete to sense a transition.
The same mini-column is capable of sensing a vast number of transitions. These mini-columns compete to “be the one” to recognize the local transition feature in the macro-column. . In my post on Hex-grids I postulate that layer 2/3 is hitting on fixed patterns and that there is a form of voting going between layers in the mini-column. (temporal and spatial patterns)
In any case - the feature recognizers compete to signal that they are “the one” to win in this macro-column. Here is where I differ from the the HTM canon - HTM as written picks a winner based on some sparsity metric; every macro-column is an island of recognition.
In my Hex-grid proposal the competition between potential grid forming pattern recognition binds the local recognition to adjacent patterns and sparsity is a natural by-product.
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