Day 8, Thurs, Feb 22, 2018

Quizzes

Next Tuesday's will focus on numpy. See Day 7 notes.

Social

Meet someone new

Vectorizing computations with numpy

avoid Python loops

vectorize creation of mayfly diagram (hint)

Butterfly Effect

st_butterfly_conservation.jpg

sensitive dependence on initial conditions

t=0

earth_from_space_1.jpg earth_from_space_1.jpg

Butterfly flaps its wings in rightworld, not in leftworld.

Two weeks later ...

t = 1

earth_from_space_3.jpg earth_from_space_2.jpg

precise definition

graph of x vs t for specific b

separation of nearby trajectories

characterization of separation

Report 2

Exploration of the dynamics of the mayfly population model

Floating-point number representation and arithmetic

We've been using a representation of the real numbers without knowing or thinking much about it.

A sensible scheme for computing in the real numbers (as opposed to integers)?

Rationals are dense in the reals: how about mayfly model in exact arithmetic?

Approximate representation in 64 bits