I built all logic gates using the bucket/fill tool. These were combined to make an 8-bit ripple-carry adder as well as an 8-bit adder/subtractor circuit.

Here's the animations of some of the circuits: https://imgur.com/a/0IbAr23

How it works:

1. Define inputs A and B (white = 0, black = 1) using bucket fill.
2. To run the circuit/computation, use the colour picker and fill tool to cycle through a sequence of colour changes from the “Bus” and “Probe” squares on the left and apply them to the circuit leads on the right.
   

This is where my knowledge of computer science ends, and I'm not sure how far this could theoretically be taken.

There are a few quirks that make this particularly challenging. For example, all logical components of the circuit are single-use (i.e., at the end of the computation, the entire circuit is black/white, and all the colour pixel logic is lost). Also, because this is in 2-dimensions it's not possible to cross/bridging/tunnel "wires" to make complex compound logic gates (XOR and XNOR). There's also a challenge with back-propagation, where colour fills don't just go forward down the circuit, but travel back and affect other parts of the circuit.