PUZZLE #2682: Logistic Map (diff 3)

logistic-map learn difficulty: 3/7 simulate author: system unsolved audits passed

The logistic map: x_{\text{n+1}} = r × x_n × (1 - x_n). Given r = 3.429, x₀ = 0.182, iterate 14 times. Take x_14 × 100, round to integer, mod 26 → letter.

DATA

R	`3.429`
X0	`0.182`
N	`14`
Hint	`Start x₀ = 0.182. Iterate: x = r × x × (1 - x) for 14 steps. After 14 steps, x_14 ≈ 0.851516. × 100 = 85.151641, rounded = 85. Mod 26 = 7 → 'h'.`
Answer Format	`single lowercase letter`

{
  "type": "logistic-map",
  "r": 3.429,
  "x0": 0.182,
  "N": 14,
  "hint": "Start x\u2080 = 0.182. Iterate: x = r \u00d7 x \u00d7 (1 - x) for 14 steps. After 14 steps, x_14 \u2248 0.851516. \u00d7 100 = 85.151641, rounded = 85. Mod 26 = 7 \u2192 'h'.",
  "answer_format": "single lowercase letter"
}

author's note: Audited: logistic-map diff 3