Chaos & Iteration in Spreadsheets: The Logistic Map, Fixed Points & Fractals
Explore chaos the hands-on way: iterate functions down a column, test fixed points with |f′(x*)| < 1, watch the logistic map converge, cycle and turn chaotic (with a chart), build a bifurcation table and diagram, measure sensitive dependence and the Lyapunov exponent, model a fish stock with the Ricker map and harvesting, and draw a Mandelbrot set from escape-time counts with a recursive LAMBDA and a colour scale – 8 labs, every cell checked instantly.
The first lesson is free — no account needed.
About this course
A chaos and iteration course that explores dynamical systems one formula copied down at a time in a spreadsheet, for maths and physics students, teachers and curious analysts who want to see chaos instead of reading about it. You iterate a linear map and the cosine map and count the steps to a fixed point, test fixed points of the logistic map for stability with |f′(x*)| < 1, iterate the logistic map for three growth rates and chart convergence, a 2-cycle and chaos, record long-run values for ten growth rates and draw a bifurcation diagram with an estimate of Feigenbaum's constant, follow two orbits that start a millionth apart, estimate the Lyapunov exponent, model a fish stock with the Ricker map and harvesting, and draw a small Mandelbrot set from escape-time counts with a recursive LAMBDA and a colour scale. The first lab is free.
Lessons
- Iterating a Function: Recurrences Copied Down & the Cobweb IdeaFree
- Fixed Points & Stability: the Test |f′(x*)| < 1 Pro
- The Logistic Map for Different r: Convergence, a 2-Cycle & Chaos (with a Chart) Pro
- Period Doubling & a Bifurcation Table: Long-Run Values for Each r Pro
- Sensitive Dependence: Two Starting Points a Millionth Apart Pro
- The Lyapunov Exponent: Averaging ln|r(1 − 2x)| Along an Orbit Pro
- Population Models: the Ricker Map, Oscillations & Harvesting Pro
- Mandelbrot & Julia Sets: Escape-Time Counts, an Area Estimate & a Colour Scale Pro