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r=1/2-1/2 cosθ Can you find the area of the main cardioid of the Mandelbrot Set?

r=1/2-1/2 cosθ Can you find the area of the main cardioid of the Mandelbrot Set?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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r=1/2-1/2 cosθ

Can you find the area of the main cardioid of the Mandelbrot Set?

In[58]== PolarPlot Cos [x], {x, 0, 2 n}| 2 - 2 0.6 0.4 - 0.2 Out[58]= -1.0 -0.8 -0.6 -0.4 -0.2 -0.2 -0.4 -0.6
Transcribed Image Text:In[58]== PolarPlot Cos [x], {x, 0, 2 n}| 2 - 2 0.6 0.4 - 0.2 Out[58]= -1.0 -0.8 -0.6 -0.4 -0.2 -0.2 -0.4 -0.6
The main cardioid of the Mandelbrot set (the largest heart-shaped region) gives the set of c-values where the orbit is not only bounded, but also eventually approaches a limit – getting closer and closer to a single fixed value. Despite the complex appearance of the Mandelbrot set in general, this region has a nice description in polar coordinates, as it is bounded by the curve* r = 2 - 2 cos e Exercise 5: Can you find the area of the main cardioid of the Mandelbrot Set? * In this formula, the origin is actually shifted from (0,0) to (¼, 0), so that really x = ¼ + rços0. y = rsinO, as usual.
Transcribed Image Text:The main cardioid of the Mandelbrot set (the largest heart-shaped region) gives the set of c-values where the orbit is not only bounded, but also eventually approaches a limit – getting closer and closer to a single fixed value. Despite the complex appearance of the Mandelbrot set in general, this region has a nice description in polar coordinates, as it is bounded by the curve* r = 2 - 2 cos e Exercise 5: Can you find the area of the main cardioid of the Mandelbrot Set? * In this formula, the origin is actually shifted from (0,0) to (¼, 0), so that really x = ¼ + rços0. y = rsinO, as usual.
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