Press space to begin. This is a zero-dimensional cellular automaton. You're probably wondering how this works, and how such a concept is even possible. Rule 90, one of the simplest of CAs, is one-dimensional. This means that the data it uses is contained within a one-dimensional array. In two-dimensional CAs, a system is used that interprets a one-dimensional array as being in the second-dimension. This is the first zero-dimensional CA that I've ever seen. I was originally planning on recreating an existing CA, but was unable to find one. So, I thought up an algorithm that would allow such a thing to be possible. Before I can begin, here's a very brief explanation on how the zeroth dimension looks: it's a point. No length, no width, no depth, no dimensions. Just a single, infinitely small point. However, you can't have an infinitely small list in Scratch. The shortest you could possibly have would be a single item/variable, which is exactly what I've done...sorta. So, here's how my system works: There's two input fields: the Seed and the Rule. The Seed represents the first two states of the variable, 1 or 0. There are 4 possible seeds, 00, 01, 10, and 11. Due to the fact that Scratch's variable sliders only uses normal numbers, I have converted these 4 seeds into decimal. 00 is 0, 01 is 1, 10 is 2, and 11 is 3. Next, the Rule. In order for the next state to be calculated, a rule is applied to the two previous states. This rule is also known as a logic gate. The previous states are funneled into the rule function, and a single response, 1 or 0, is returned. Like the Seed, I've converted the 16 possible responses into decimal form as well. Here's an example of the XOR gate, which responds with 1 if either of the two inputs are 1, but not both: 0110 (6) In order to display the current state, I've used the pen tool. Black represents 1, and white represents 0 (going from top to bottom). That's all that there is! If you're good with truth tables, this will be easy for you.
