Buffalo iteration
The squared coordinate magnitudes make the real part: xₙ₊₁ = |xₙ|² − |yₙ|² + Re(c). The imaginary part pairs signed xₙ with folded yₙ: yₙ₊₁ = 2·xₙ·|yₙ| + Im(c). The difference from Burning Ship sits exactly there: Buffalo folds squared terms one by one, rather than folding raw coordinates before squaring. Keeping xₙ signed preserves a directional imbalance that Burning Ship’s fully folded cross term erases.
Try c = −0.5. Starting from z₀ = 0, the first iteration gives z₁ = |0|² − |0|² + 2i·0·|0| − 0.5 = −0.5. The second iteration: z₂ = |−0.5|² − |0|² + 2i·(−0.5)·|0| − 0.5 = 0.25 − 0.5 = −0.25. The orbit settles into a bounded oscillation between negative real values. With the same c, Burning Ship gives (|−0.5| + i|0|)² − 0.5 = 0.25 − 0.5 = −0.25 at the second step; the paths already differ because it folded the real part before squaring.
