Feigenbaum Constant Calculator
Free online feigenbaum constant calculator. Enter your values and get instant results with the formula, step-by-step working, a worked example and FAQs — everything runs locally in your browser on Calcton, no signup required.
中文版：费根鲍姆常数在线计算器
逻辑斯谛映射 x ↦ a·x(1−x) 随 a 增大经历倍周期级联：稳定周期 2 → 4 → 8 → …。每一层的「超稳点」aₙ 定义为 2ⁿ 次迭代把临界点 1/2 恰好送回 1/2 的参数。费根鲍姆 1975 年发现：相邻超稳参数的间距比 (aₙ − aₙ₋₁)/(aₙ₊₁ − aₙ) 收敛到同一个普适常数 δ = 4.669201609102990——它对一切「单峰」映射成立（正弦映射、Ricker 模型、圆映射），与具体函数形状无关，是混沌理论中的普适性定理。
数值上对每个 n 用符号二分：f^(2ⁿ)(1/2) − 1/2 在超稳参数处穿零，n ≥ 4 的搜索窗口按间隙比 ×[0.16, 0.30] 收缩（间隙比趋于 1/δ ≈ 0.214）。比值 δₙ 的误差按 δ^(−n) 速率收敛，所以前几层只吻合三到四位，n = 9、10 时进入第六位以上。
参考值
a₁ = 2，a₂ = 1+√5 = 3.236067977499790，a₃ = 3.498561699327040
a₄ = 3.554640862768813，a₈ ≈ 3.5699135，a∞ = 3.569945671870945
δ = 4.669201609102990（普适），α = 2.502907875095892（标度因子）
How to use the Feigenbaum Constant Calculator
- Fill in the inputs with your own numbers — every field shows what it expects.
- The result updates instantly as you type; no "Calculate" click needed.
- Read the result card for the main figure, the step-by-step formula, and practical notes.
Frequently asked questions
Is the Feigenbaum Constant Calculator free?
Yes — all math calculators on Calcton are free, with no sign-up required. Your inputs are processed in your browser and never sent to a server.
Is there a Chinese version of this tool?
Yes. Use the Chinese version link above — it is the same calculator with the interface in Simplified Chinese.
References
Formulas and benchmarks used by this calculator follow these published sources.
KevinContent LeadCalcton Editorial Team · Last updated 2026-09-27
Kevin maintains Calcton's formula verification and content: every calculator cites the standard it implements, worked examples are recomputed programmatically, and health benchmarks follow WHO and international guidelines.
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