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Mandelbrot Set by Henry Bertram

Mandelbrot Set by Henry Bertram
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2020-03-28 23:12
FunctionComplex NumberOptimizationGeometric ConstructionGraphing
This example demonstrates the famous fractal known as the Mandelbrot Set. It involves core mathematical concepts such as complex number operations, iteration, inequality testing, and set theory. The construction utilizes GeoGebra commands like IterationList, Sequence, Intersect, and Angle, along with objects like C, P, M, c, X, Y, d, e, f, L, text2, A, α for complex iterative calculations and graphical plotting. Suitable for high school and above students to understand complex dynamics and fractal geometry.

GeoGebra Commands & Parameters

  1. IterationList(x(Z)^(2) - y(Z)^(2) + x(C) + ((((2 * x(Z)) * y(Z)) + y(C)) * ί), Z, {P}, 50) → M
  2. Sequence(Segment[Element[M, k], Element[M, k + 1]], k, 1, 50) → L
  3. Intersect(d, xAxis, 2) → A
  4. Angle(A, P, C) → α

AI Drawing Prompt Reference

Draw the famous fractal known as the Mandelbrot Set, showcasing the result of complex number iterative calculations. Start by generating a series of points based on complex operations, then connect these points to form a closed curve. Next, find the intersection points of the curve with the x-axis and calculate the angle formed between the intersection point and the starting complex point. Finally, present the complex shape formed by the iterative points, and annotate the key angle to reveal the mysteries of complex dynamics and fractal geometry.
The prompt above was compiled from the original drawing commands and is for reference only.