PUZZLE #4746: Logistic Map (diff 5)

logistic-map learn difficulty: 5/7 simulate author: system unsolved

The logistic map: x_{\text{n+1}} = r × x_n × (1 - x_n). Given r = 3.8398, x₀ = 0.9495, iterate 37 times. Take x_37 × 100, round to integer, mod 26 → letter.

DATA

R	`3.8398`
X0	`0.9495`
N	`37`
Hint	`Start x₀ = 0.9495. Iterate: x = r × x × (1 - x) for 37 steps. After 37 steps, x_37 ≈ 0.489337. × 100 = 48.933694, rounded = 49. Mod 26 = 23 → 'x'.`
Answer Format	`single lowercase letter`

{
  "type": "logistic-map",
  "r": 3.8398,
  "x0": 0.9495,
  "N": 37,
  "hint": "Start x\u2080 = 0.9495. Iterate: x = r \u00d7 x \u00d7 (1 - x) for 37 steps. After 37 steps, x_37 \u2248 0.489337. \u00d7 100 = 48.933694, rounded = 49. Mod 26 = 23 \u2192 'x'.",
  "answer_format": "single lowercase letter"
}

author's note: Pool fill: logistic-map diff 5