Day 16, Thursday, Mar 29, 2018

Newton's method as a dynamical system

Complex numbers

Let's invent a new arithmetic ... on objects (x,y)

addition, subtraction

strange but useful multiplication, identity

division: multiplicative inverse

real arithmetic embedded

(0,1)*(0,1) and (0,-1)**2

polar rep, where multiplication looks simple (modulus)

cube roots of (1,0)

Interlude on color

color.png

RGB color: pixels

lcd_screen.png

(whole photo)

Exercise

Replicate this:

color_exercise.png

Visualizing Newton dynamics on f(z) = z3 − 1

graph of a complex function?

numpy.meshgrid