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All About F

Fig Trees and Butterflys

Systems like the weather, population growth, chemical reactions, and snowflake formation all have something in common: small changes in the starting conditions create huge changes in the final outcome.

This is because each stage depends only on the previous stage, so small differences get amplified into big differences. We call these systems chaotic, because the final outcome is so unpredictable.

Chaos Discovered

When Mitchell Feigenbaum was looking at animal populations in the mid 1970’s, he found that the population size was predictable only when a certain constant describing the birth and death rate was small, but it became chaotic when this constant was increased beyond a certain point. By studying this system, Feigenbaum discovered a fundamental value, now called Feigenbaum’s constant, that can be used to predict the point at which any such system becomes chaotic.

Trivia

  • Feigenbaum means “fig tree” in German.
  • Feigenbaum solved for his constant using an HP-65, the first fully programmable, handheld calculator. This calculator was also used by astronauts in the final Apollo mission.
  • Every snowflake is unique, because snowflake formation is chaotic.
  • The Butterfly Effect describes the surprising results of weather being chaotic.
  • Feigenbaum’s constant also appears in the fractal created by the Mandelbrot set.