23. Mandelbrot - ENGR 101, Section 100, Fall 10 Fractals...

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ENGR 101, Section 100, Fall 10 M. Wellman 1 Fractals and the Mandelbrot Set ENGR 101, Lecture 23: 8 Dec 10 Announcements Project 8 due Mon 13 Dec Exam 3 Thu 16 Dec, 8–10am open book & notes no computation or communication devices similar format to previous exams Course evaluations (coming up on CTools)
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ENGR 101, Section 100, Fall 10 M. Wellman 2 How Long is the Coastline of Michigan (L.P.)? 8.7 units 9.5 units A: It depends on the size of your ruler Fractals Geographic shape exhibiting self-similarity Parts maintain characteristics of the whole, in reduced size Name and definition due to mathematician Benoit Mandelbrot Most famous fractal: the Mandelbrot set 1924-2010
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ENGR 101, Section 100, Fall 10 M. Wellman 3 Fractal Boundary of the Mandelbrot Set Generating the Mandelbrot Set Consider the family of recurrence equations : z 1 = 0 z m + 1 = z m 2 + c c 1 0.1 z 1 0 0 z 2 1 0.1 z 3 2 0.11 z 4 5 0.1121 z 5 26 0.1126 z 6 677 0.1127 z 7 458330 0.1127 Grows very quickly for c = 1 very slowly for c = 0.1
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ENGR 101, Section 100, Fall 10 M. Wellman 4 The Mandelbrot Set (Definition) Let c be a complex number
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This note was uploaded on 05/25/2011 for the course ENGR 101 taught by Professor Ringenberg during the Fall '07 term at University of Michigan.

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23. Mandelbrot - ENGR 101, Section 100, Fall 10 Fractals...

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