Apa itu Konstanta Feigenbaum?

Period-doubling cascade: each bifurcation requires 4.669× less r-space (δ)

The logistic map xₙ₊₁ = r·xₙ(1−xₙ) doubles its period at r≈3.0, 3.449, 3.544, 3.5644… Each gap is δ≈4.669 times smaller (Feigenbaum constant).

card_02

δ appears in unrelated physical systems: it is truly universal

Table showing Feigenbaum constant measured in different physical systems

System	Gemessenes δ
Logistische Abbildung (Theorie)	4,66920 (exakt)
Tropfender Wasserhahn	4,5 ± 0,3
Elektronische Schaltkreise	4,66 ± 0,02
Konvektion in Fluiden	4,4 ± 0,5
Herzrhythmen	≈ 4,6

Cobweb diagram: iterating the logistic map xₙ₊₁ = r·xₙ(1−xₙ)

xₙ₊₁ = r · xₙ · (1 − xₙ)

At r=3.2: iterates settle into a 2-cycle (0.513 ↔ 0.799)

At r=3.5: 4-cycle. At r=3.57: 8-cycle. At r>3.57: chaos

Cobweb: draw vertical to curve, horizontal to y=x, repeat – reveals the orbit

linkscard_04

Digunakan dalam

∑Matematika

✓

⚛Fisika

✓

⚙Teknik

✓

🧬Biologi

–

💻Ilmu Komputer

–

📊Statistika

–

📈Keuangan

–

🎨Seni

–

🏛Arsitektur

–

♪Musik

–

🔐Kriptografi

–

🌌Astronomi

–

⚗Kimia

✓

🦉Filsafat

–

🗺Geografi

–

🌿Ekologi

✓

Want to test your knowledge?

Question

Apakah konstanta Feigenbaum rasional, aljabar, atau transendental?

tap · space

1 / 10

Siap bermain?

Pi

Memorize pi, e, and 40+ mathematical constants using the numpad path method

Main sekarang - gratis

Tanpa akun. Bisa di perangkat apa saja.