This equation will change how you see the world (the logistic map)

Summary by Krater

This video explains the logistic map equation and how it leads to period-doubling bifurcations and chaos, demonstrating how a simple non-linear feedback loop models phenomena from rabbit populations and fluid convection to heart fibrillation and flickering lights.

From the video

Answers: What is the connection between a dripping faucet, rabbits, and chaos theory?

• logistic map
• period-doubling bifurcations
• chaos theory
• fractals
• Mandelbrot set
• Feigenbaum constant
• fluid convection
• heart fibrillation

What it concludes

• A simple non-linear equation with negative feedback can produce period-doubling bifurcations that lead to chaos as the growth rate increases.
• Bifurcation diagrams derived from logistic and sine maps are actually part of the Mandelbrot set.
• The ratio of the widths of bifurcation sections converges on the Feigenbaum constant of approximately 4.669 across different non-linear systems.
• Chaos theory can be applied in real time to determine when to deliver electrical shocks to a heart in fibrillation to restore periodicity.