Lecture 5 (Fractal Geometry and Landscapes)

Question 1

WTF is a ‘Fractal’?

Answer 1

A geometric shape generated using a series of recursive rules
- i.e. has a pattern that repeats at different scales (self-similarity)

Question 2

What are some manifestations of fractals?

Answer 2

Nature, geometry, computer graphics, cinema, etc.

Question 3

Approaches to generating 3D landscapes with fractals?

Answer 3

• Brownian motion

- Diamond-square algorithm

Question 4

WTF is ‘Brownian Motion’?

Answer 4

Used to make landscapes through random movement of particles e.g. pollen in water

• Creates a natural randomly generated landscape

Question 5

WTF is ‘Diamond-Square Algorithm’?

Answer 5

Used to make landscapes through alternating between diamond & square steps

• Each time random variable is changed -> makes it look more natural

Question 6

Elaborate on self-similarity

Answer 6

exact (strongest), quasi, statistical (weakest)

Question 7

What is Exact Self-Similarity?

Answer 7

The fractal appears identical at different scales

• This is the strongest

Question 8

What is Quasi Self-Similarity?

Answer 8

The fractal appears approximately (but not exactly) identical at different scales
- Contain small copies of the entire fractal in distorted and degenerate forms

Question 9

What is Statistical Self-Similarity?

Answer 9

Certain statistical properties are repeated. Differences are based on statistical algorithm

• This is the weakest

Question 10

Why would typical basic primitives (lines, circles, polygons) not be suitable for fractals?

Answer 10

Would need millions of these to work

Question 11

How does the Diamond-Square Algorithm work?

Answer 11

• Start by setting the initial values for the corner points of the grid
• Alternate between performing a diamond step and a square step until completion.
• Diamond Step: for each square in the array, set the midpoint of that square to be the average of the intersecting points plus a random value
• Square Step: for each diamond in the array, set the midpoint of that diamond to be the average of the intersecting points plus a random value