this is messy, im sorry

a boolean network is an evolving system that comprises:
1. a set of nodes which each just hold a binary (boolean) value, zero or one, on or off
2. a transition function, that has a randomly specified output state corresponding to every combination of the nodes

the transition function for a single node in a 2 node system might look like

| state of all nodes | output of this node |
| ------------------ | ------------------- |
|                 00 | 1                   |
|                 01 | 0                   |
|                 10 | 1                   |
|                 11 | 1                   |

where the output bits are completely randomly specified. like here, if the state of the network is 10, then our node's output (this could be any one of those two nodes) would become 1 in the next state of the network. each node has a transition function like this

for 2-node networks, there are 256 possible transition functions (four possible states times two nodes is eight values that can be one of two states, so 2^8=256 defines our number of possibilities) but if we take every possible state for a network, draw a little circle for each one and add lines between the states that can transition to or transition from eachother, there's actually only 18 different possible shapes we can get out (if we push the nodes around a bit to look clean, without breaking any lines)



i think problems and concepts in general might be the same way, there are tons of possible concepts and problems but if we make graphs (the shapes) out of relations (the lines) between specific components of your concept or problem (the states / circles) we might only get a few possible shapes out

i think that maybe good analogies are defined by graphs of relations between components of concepts having as similar of shapes as possible, and that when you are problem-solving you might be able to unconsciously compare the shape of what you know about in your problem to the shapes of other problems, and that *in* the shapes of other problems that have obviously similar structures you might be able to see structures that are currently missing from your understanding your problem