Mandelbrot & Julia Sets: Escape-Time Counts, an Area Estimate & a Colour Scale
This lesson is part of the course
In this lesson
You 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.
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Lessons in this course
- Iterating a Function: Recurrences Copied Down & the Cobweb Idea Locked
- Fixed Points & Stability: the Test |f′(x*)| < 1 Locked
- The Logistic Map for Different r: Convergence, a 2-Cycle & Chaos (with a Chart) Locked
- Period Doubling & a Bifurcation Table: Long-Run Values for Each r Locked
- Sensitive Dependence: Two Starting Points a Millionth Apart Locked
- The Lyapunov Exponent: Averaging ln|r(1 − 2x)| Along an Orbit Locked
- Population Models: the Ricker Map, Oscillations & Harvesting Locked
- Mandelbrot & Julia Sets: Escape-Time Counts, an Area Estimate & a Colour Scale Locked