I understand intuitively that gear bits in the massively successful Turing Tumble game (funded by kickstarter) are necessary for Turing completeness*.
I had a fantasy about building a computer with the Lego racetracks which have Y junctions operated by gates. Going into a branching path, the gate controls the car's path, and going the opposite direction the car flips the gate. If you linked the gates together, it could be Turing complete. It's a different twist on the same idea as Turing Tumble.
No matter my intuitive grasp, I couldn't adequately explain to a coworker why this linking is necessary.
Here's a diagram of classes of automata. In a formal but understandable manner, please explain to which class Turing Tumble without gear bits belongs to* and why. With gear bits, explain why Turing Tumble becomes Turing complete*.
* up to memory constraints