Temporal memory and synapses initialization

Hi , i am new in HTM theory .
I am building an implementation in matlab (for temporal memory) and i try to understand how ,for t=1 (first input) the synapses initiliaze. Correct if i am wrong,but pseudocode(BAMI) tells that if for a cell that belongs in an activated column there is not a segment with active synapses above activationThreshold (of course in t=1 there is none) ,add random synapses to cells with learnstate=1.In t=1 ,there are not such cells (correct me again if i am wrong).So how are first synapses initialized?
Thanks in advance

The first input (or an input after a reset) should not generate any new synapses. The second input will connect with the first input, and so-on.

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I read that when a cell becomes active it starts forming synapses with neighbor cells .So , after reset for example (as you say) synapses grow for each active cell (in time : t=k) with neighbour cells(defined by user or algorithm ?) that where active in
t=k-1 ?
I am just a little bit confused by how first segment of synapses should be initialized.

If there was no activity at t=k-1, or there was a reset between t=k-1 and t=k, then no synapses are formed. If there was activity at t=k-1, then synapses are formed to a subset of the activity at t=k-1.

I’m currently brainstorming about this topic for the next HTM School episode. If anyone has any ideas about visualizing this, please share. I want to show more how bursting works to kick off sequences, and what a rest actually does.

Some ideas that came quickly : I think that it would be helpful if the visualization shows how segments and synapses grow , starting from first time step.Also if it is possible , the adaptation steps for synapses (weight increment/ decrement ) for some time steps.I don’t know if it is possible to show these simultaneously (one array for weights,one for activated synapses for all cells etc) .