"tH.........\n.   .\n   ...\n.   .\nHt.. ......"
CanBeHead ← ⍥₂(⍉↘¯1↘1)⬚@\s⧈(↥⊃=₁=₂/+=@H⍜⊡₄⋅@./⊂)3_3
Successor ← ⍣(@\s◌ °@\s|@t◌ °@H|@.◌ °@t|@H °1◌|@.)
Step      ← ≡₋₂Successor⟜CanBeHead
⍥⊸Step20 ⬚@\s⊜∘⊸≠@\n
▽10≡▽₂20≡₋₃(⍣(0_0_0 °@\s|1_0_0 °@H|0.9_0.7_0 °@t|÷3 1_1_1))