Edit the rules, then let the machine loose.
Each rule says: when the head reads 0 or 1 in a state, write a symbol, move left or right, and choose the next state. Reaching H halts the machine.
Rule table
Tip: build a small machine by changing one rule at a time, then use Step so the logic stays visible.
Challenge prompt
The 2-state champion prints four 1s in six steps. Can your altered rules halt with more, or do they run forever? There is no general shortcut that can always tell us.
Small state counts, absurd outcomes.
Busy Beaver values grow faster than any computable function. Known exact values stop early, because proving a machine eventually halts can become harder than running it.
steps for the known 5-state value
Two symbols, a finite list of states, one tape head, and local rules. Nothing mystical is hidden in the model.
Among machines that halt, which one writes the most 1s? The word “halts” carries the whole weight.
Busy Beaver turns the halting problem into something you can watch move cell by cell.