Feigenbaum constants

The Feigenbaum constants are two special mathematical numbers discovered by Mitchell Feigenbaum that describe how complex, chaotic systems—like weather patterns or populations—transition from orderly to chaotic behavior. The first constant, approximately 4.669, measures how quickly these systems’ behaviors repeat in a pattern called bifurcation as a control parameter changes. The second, about 2.502, relates to the ratio of distances between these bifurcations. These constants reflect a universal pattern across many different systems, revealing that chaos often follows predictable mathematical rules.