-
-
Welcome and Overview
-
Self-Similarity Dimension
-
Some Properties and Features of Fractals
-
Exponent and Logarithm Review (Optional)
-
Video (10:00) Exponent Properties
-
Quiz 1: Exponent Properties
-
Quiz 2: More Exponent Properties
-
Video (5:50) Logarithm definition
-
Quiz 3: Logarithm Basics
-
Solution to Quiz 3 (5:00)
-
Video (5:40) Logarithm properties
-
Quiz 4: Logarithm properties
-
Solution to Quiz 4 (2:01)
-
Video (2:16) Using logarithms
-
Quiz 5: Using logarithms
-
Solution to Quiz 5 (4:55)
-
Video (4:04) Logarithms: different bases
-
-
Summary
-
Homework (Optional)
-
Test
-
-
-
Introduction
-
Fractals via Deterministic Iteration
-
Adding a Bit of Randomness
-
The Chaos Game
-
Diffusion-Limited Aggregation
-
Summary
-
Programs and Resources
-
Homework (Optional)
-
Test
-
-
-
Introduction
-
Basic Box-Counting
-
Box-Counting in Practice
-
Video (8:39) Introduction: s must be small
-
Video (15:08) Box-counting a circle
-
Quiz 1: Box-counting the Koch curve
-
Quiz 2: The dimension of the Koch curve
-
Video (7:26) Log-log plots
-
Video (11:31) Log-log plot for a square
-
Quiz 3: Log-log plots
-
Video (2:10) Solution to quiz 3
-
Video (11:03) Log-log plots: practicalities and issues
-
-
Thinking about Dimensions
-
Summary
-
Homework (Optional)
-
Test
-
-
-
Introduction
-
An Initial Example: Word Frequency
-
Other Distributions
-
Properties of Power Laws
-
When do Averages Exist?
-
Interview: Nick Watkins
-
Summary
-
Homework (Optional)
-
-
-
Introduction
-
Cumulative Distributions and Rank/Frequency Plots
-
Estimating the Exponent
-
Other Long-tailed Distributions
-
Summary
-
Additional Resources
-
Homework (Optional)
-
Test
-
-
-
Introduction
-
Rich-get-Richer Models
-
Combinations of Exponentials
-
Multiplicative Processes
-
Optimization
-
Phase Transitions?
-
Homework (Optional)
-
Additional Resources
-
Test
-
-
-
Introduction
-
Metabolic Scaling
-
WBE Theory of Metabolic Scaling
-
Interview: Van Savage
-
Interview: Geoffrey West
-
Additional Resources
-
Homework (Optional)
-
Test
-
-
-
Introduction
-
Empirical Results
-
A Theory of Urban Scaling?
-
Interview: Christa Brelsford
-
Interview: Luis Bettencourt
-
Homework (Optional)
-
Test
-
Additional Resources
-
-
-
Summary
-
Farewell
-
2.2 Fractals via Deterministic Iteration » Explorations
Use the program at http://www.shodor.org/master/fractal/software/Snowflake.html to determine the fractal that results from iterating the following substitutions:
1.
2.
For this one, be sure that the line segments on the right are all the same size. On the program, choose a triangular grid and make sure 'snap to grid' is selected.
3.
