mandelbrot - How to define the Mandelbrot set Math 8 2009,...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: How to define the Mandelbrot set Math 8 2009, Chris Lyons The famous Mandelbrot set is a subset of the complex plane: The black points signify the members of the Mandelbrot set. Fix a number c in the complex plane. Here’s how we tell if c belongs to the Mandelbrot set or not: STEP 1: Define z0 = 0. STEP 2: For each n ≥ 0, define 2 zn+1 = zn + c. In other words, we let z1 = c z2 = c2 + c z3 = (c2 + c)2 + c z4 = ((c2 + c)2 + c)2 + c etc... STEP 3: The sequence {zn } is just some sequence of complex numbers, and we care about the size—i.e., the complex absolute value—of the numbers zn as n → ∞. • IF the sequence {zn } is bounded, i.e., if there is some R such that |zn | ≤ R for all n, then we say c belongs to the Mandelbrot set. • IF NOT, then we say that c does not belong to the Mandelbrot set. That’s it! 1 ...
View Full Document

This note was uploaded on 07/19/2010 for the course MA 1C taught by Professor Ramakrishnan during the Spring '08 term at Caltech.

Ask a homework question - tutors are online