According to this source, a neuron can connect to up to 10,000 other neurons. Does this imply that neurons are clustered, that is, not evenly spaced? Argument:
Say axons are length $L$, and dendrites are length $D$. Say a neuron $N$ has 10,000 outgoing connections. Then there must be 10,000 neurons within distance $D$ of $N$'s axon terminal. Then each of those 10,000 neurons are within distance $2D$ of each other by the triangle inequality. Assuming $2D<L$, then all of those 10,000 neurons are less than an axon's distance from each other. But for this to be true, the 10,000 neurons must be closer to each other than they are to $N$. Since this argument holds for any neuron, we get the result that neurons must form clusters of around $10,000$ neurons, or their dendrites must be longer than half their axon length.
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