period-three · not in domain-math.js · 9 records · all concepts
runs7 · +2 retired
114For a hierarchical lattice whose rule is a Boolean function f on k independent children, the RG map is R(p) = Σ_j c_j p^j (1 − p)^{k−j} with c_j the number of accepted inputs of weight j, 0 ≤ c_j ≤ C(k, j).run
117On the exclusive hierarchical rules of run 114 (not-all-equal and the band rules [a, b], k = 2 … 12), does the distance to period three O(R) increase with k along NAE, and is the stretch |λ| at the interior fixed point above 1.8 on every rule that has a period-3 orbit?run
123Off the entropy plateaus, does the Li–Yorke slack O₂ rank the period-3 band rules at each k as their topological entropy does?run
124Is the Li–Yorke slack O₂ a reading of the period-3 saddle-node's unfolding, ranking the period-3 band rules at each k as the split between their two 3-cycles' multipliers does?run
125On the continuous band family, is the stable-born 3-cycle's multiplier at or below −8 at every point where the map reaches the log 2 ceiling, the crisis R²(c) = q?run
128Past k = 30, does the band family's closest approach to −8 at the crisis keep approaching from below at the rate k⁻², while the other cycle approaches +8 at the slower rate k⁻¹?run
129At k = 72 to 128, do the closest approach's four scaled quantities extrapolate to the derived limits, d₋k² → 27.2532, d₊k → 8.28684, (b − a)/√k + k^{−1/2} → 0.931582 and (a + b)/(2k) → 0.683325?run
120With the distance to period three measured on the map's core in both orientations (O₂), is O₂'s sign exactly the period-3 test on run 114's 286 exclusive rules, and does O₂ increase along the not-all-equal rules?run
121Does O₂'s sign — the Li–Yorke slack on a hump map's core, in either orientation — separate period three exactly on hierarchical rules no run has computed: the NAE and band rules at k = 13 … 16, and random rules from the full box at k = 7 and 8?run
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