Polar Coordinates Example 2
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Visualization of limits of functions of two variables
This example demonstrates how to draw complex fractal patterns using polar coordinates by adjusting parameters dynamically. Core math concepts include polar coordinate systems, trigonometric functions, iterative functions, and fractal geometry. GeoGebra commands/objects used are f (function), r (radius), a (angle parameter), and b (iteration count). Suitable for high school and above learners to understand polar coordinate applications and fractal generation principles.
GeoGebra Commands & Parameters
f(x, y) = ((2 * x^(2)) * y / (x^(4) + y^(2)))Numeric r(1.49)a(x, y) = x^(2) + y^(2) ≤ r^(2)b(x, y) = If[x^(2) + y^(2) ≤ r^(2), f(x, y)]
AI Drawing Prompt Reference
Draw a complex fractal pattern using polar coordinates. First, define a function f(x, y), then set the radius r to 1.49. Use the polar coordinate parameter a(x, y) to limit the drawing range, and finally generate the fractal pattern through the iterative function b(x, y).
The prompt above was compiled from the original drawing commands and is for reference only.