E7Lecture10Summary - E7 Intro to Computer Lecture 10...

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E7: Intro to Computer. . . Lecture 10: Iteration, Fractals. . . Tad Patzek, Civil & Environmental Engineering, U.C. Berkeley March 03, 2008
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Class announcement. . . From next week (March 3rd, 2008) until the end of the semester, labs for Sections 20, 21, 22, and 23 will take place in 212 Wheeler Hall . The time schedule is the same, only the location is different. New logins will be given to you by your GSIs during the next lab. Prof. T.W. Patzek’s E7 Lecture 10: . . . – p.1/13
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Material Covered. . . Function calls Midterm results Iteration: Mandelbrot orbits and fractal, Julia sets Prof. T.W. Patzek’s E7 Lecture 10: . . . – p.2/13
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Fractals. . . Prof. T.W. Patzek’s E7 Lecture 10: . . . – p.3/13
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Fractals. . . Prof. T.W. Patzek’s E7 Lecture 10: . . . – p.4/13
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Mandelbrot Fractal. . . A set of complex constants c for which the iteration z n +1 = z 2 n + c, n = 0 , 1 ,... z 0 = 0 does not run away to infinity Prof. T.W. Patzek’s E7 Lecture 10: . . . – p.5/13
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Mandelbrot Fractal. . . Orbits. The list of numbers z 0 ,z 1 ,z n ,... generated under iteration of z 2 + c is called the orbit of z 0 . Prof. T.W. Patzek’s E7 Lecture 10: . . . – p.6/13
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Mandelbrot Fractal. . . The Mandelbrot fractal is a set of finite (compact) orbits of zero z 0 = 0 Prof. T.W. Patzek’s E7 Lecture 10: . . . – p.7/13
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Mandelbrot Fractal. . . Start with c = 1 : z 0 = 0
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