There are 2D rules that are aesthetically similar to Rule 30 (in how reactive and "fluffy" they are, and how they tend to perpetuate instead of die down), but a 2D and a 3D rule are fundamentally different.
But you can apply simple transformations on rules, like reflecting them (1D and 2D) and rotating them (2D only), or layering them (having a bunch of lower dimension rules running in parallel). Or you can perform a 1D rule along each horizontal/vertical axis (or even diagonal axis) and then combine them somehow (like XOR). But that will typically have a vastly different behavior.
One of my favorite 2D rules that looks kind of like an animated version of Rule 30 is "HGLASS", named that because it looks kind of like the falling sand in an hourglass. If you run it in a torus (edges wrap around), it tends to settle into a circular dependency tree with gaps bubbling up through it like space between cars in a traffic jam.
This is a five-neighbor two-state two-dimensional cellular automaton found at random by Margolus and Toffoli. It organizes a nice sliding flow on a random screen, and it disassembles solid starting patterns in an interesting way.
But you can apply simple transformations on rules, like reflecting them (1D and 2D) and rotating them (2D only), or layering them (having a bunch of lower dimension rules running in parallel). Or you can perform a 1D rule along each horizontal/vertical axis (or even diagonal axis) and then combine them somehow (like XOR). But that will typically have a vastly different behavior.
One of my favorite 2D rules that looks kind of like an animated version of Rule 30 is "HGLASS", named that because it looks kind of like the falling sand in an hourglass. If you run it in a torus (edges wrap around), it tends to settle into a circular dependency tree with gaps bubbling up through it like space between cars in a traffic jam.
https://www.fourmilab.ch/cellab/manual/rules.html#HGlass
This is a five-neighbor two-state two-dimensional cellular automaton found at random by Margolus and Toffoli. It organizes a nice sliding flow on a random screen, and it disassembles solid starting patterns in an interesting way.
You can see it here:
https://donhopkins.com/home/CAM6/
1. Click the gray square in the upper right corner.
2. Click "Rules".
3. Select from the Rule dropdown "von Neumann HGlass Down".
4. Draw in the cells.
5. Click in the histogram at to to change the drawing cell value. Click "Tools" to configure the drawing tool.
6. Play around with the other variants of HGLASS (Up/Down/Left/Right, echo, heat) and parallel rules like 4 HGlass Down / All)