{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

23. Mandelbrot

# 23. Mandelbrot - ENGR 101 Section 100 Fall 10 Fractals and...

This preview shows pages 1–5. Sign up to view the full content.

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)

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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
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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
ENGR 101, Section 100, Fall 10 M. Wellman 4 The Mandelbrot Set (Definition) Let c
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern