I never worked in this field before, I just thought about this set of rules and never saw something similar before. I apologise if I don't use the right mathematical vocabulary for my question.
Imagine a graph, in which bulbs are linked. The light can whether be on or off. Bounds between bulbs are one-way. But more than one bound between two bulbs are possible.
Then there is this rule : Each time the clock ticks, the bulbs who receive light from at least two alight bulbs become lit too. The others are turned off.
For example, the previous graph will, the next time the clock ticks, become like this :
And then it will become :
I made a quick search, but I'm not used to the mathematical vocabulary of this field but I'm pretty sure it exists. Then I studied this... "set of rules" a little bit.
Before the question, here are some interesting and maybe useful circuits.
This narcissistic bulb will never get off, because it's connected to itself by two bounds.
This is an AND gate because, the bulb C will be lit (after 1 cycle) if and if only the bulb A AND the bulb B are lit.
This is an OR gate because, the bulb C will be lit (after 1 cycle) if and if only the bulb A OR the bulb B is lit.
I wanted to determine if I could build a computer with this set of rules. This is why I tried to determine the classical logic Boolean gates. But the NOT gate is essential to Boolean arithmetic, and I can't think of a way to create it or to prove it's impossible.
A NOT gate is supposed to be a circuit where if a bulb A is lit, then after a predetermined clock ticks, the bulb B will be off, and if A is off, B will be lit. A kind of inverter.
My questions are :
- How is this field named in mathematics ?
- Is it possible to create a NOT gate ?