Chaos & Iteration in Spreadsheets: The Logistic Map, Fixed Points & Fractals

What you'll build

What you will be able to do

Each lab ends with a concrete result that you build yourself and the checker confirms, cell by cell.

• Iterate a linear map and the cosine map down a column, find the fixed point of the linear map with a formula and count how many steps it takes to get within 0.01 of it.
• Find the fixed point of the logistic map for six growth rates, compute the slope there, decide with IF and ABS whether it is stable and estimate how fast the orbit settles.
• Iterate the logistic map 30 steps for three growth rates side by side, compare the 2-cycle with its exact formula and chart the three orbits.
• Record eight long-run values of the logistic map for ten growth rates, count the distinct values to read off the period, estimate Feigenbaum's constant and draw a bifurcation diagram.
• Run two orbits of the chaotic logistic map whose starts differ by 0.000001, track the gap, find when it passes 0.1 and measure its average growth per step.
• Estimate the Lyapunov exponent of the logistic map for a chaotic and a periodic growth rate by averaging the log of the slope along 100 steps, and classify each case.
• Simulate a fish stock with the Ricker model for 20 years with and without proportional harvesting, then calculate the harvested equilibrium and its stability slope.
• Iterate z² + c for one complex number with separate real and imaginary columns and count when it escapes, then turn an 11 × 11 grid of escape counts into a small Mandelbrot picture with a colour scale and estimate the set's area.