
The important part is that F is getting rewritten. The g parameter is incremented each time to act as an age attribute, so g is the linear growth, and then length is set by using g in a funky smooth step type function thingy ((-2*g^3)+(3*g^2)) to get a kinda sigmoidal growth.
The b variable is used to control the speed of the growth.
The rest is just for controlling the branching so that the l-system came to some kind of end state. Like the m parameter in A(m) which decays over generations so that it stops getting replaced eventually.
The generation parameter is just set to $F so that every frame is another full generation.
This is the same l-system without rewriting F:
hipnc is here.

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