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Created by Jordan Nakamura Mandelbrot Sets Created by Jordan Nakamura

How to use Sage Go to: www.sabenb.org in order to access the notebook Go to: http://sagemath.org in order to download SAGE. (Note: You don’t need to download SAGE to use it! You can just access the notebook online to use it!)

SAGE API located at: http://www.sagemath.org/doc/reference/ Created by William Stein (professor at UW)

Math people are cool!

Definition All the complex numbers such that: Is bounded. i.e. If then we will assume it is bounded! By definition More information on http://en.wikipedia.org/wiki/Mandelbrot_set 5

Example Complex number c = 2 + 2i So it is not bounded.

Example 2 So it is bounded. Therefore, the point (0 + 0i) is in the Mandelbrot Set.

Complex Plane It looks just like the Cartesian coordinate plane, except the “x-axis” is the real numbers and the “y-axis” is the imaginary parts. Real numbers are complex numbers without the “imaginary” part. Complex number = 2 + 3i real imaginary

This is the point (35 + 40i) This is the point (-20 + 15i)