Watch Current Video List All Videos ✓ Introduction to Fractals and Dimension All Unit 1 Files Forum for Unit 1 ✓ Welcome and Overview ✓ Video (3:24). Welcome to the course Download Video Subtitles & Transcripts ✓ Video (4:27). Introducing fractals Download Video Subtitles & Transcripts ✓ Self-Similarity Dimension ✓ Video (9:07). Dimension for non-fractals Download Video Subtitles & Transcripts ✓ Quiz 1 ✓ Solution to Quiz 1 (1:54) Download Video Subtitles & Transcripts ✓ Video (8:44). Dimension of fractal "snowflake" Download Video Subtitles & Transcripts ✓ Video (4:24). Dimension of Sierpiński triangle Download Video Subtitles & Transcripts ✓ Quiz 2: The Koch Curve ✓ Quiz 3: A variant on the Sierpiński triangle ✓ Solution to Quiz 2 (2:55) Download Video Subtitles & Transcripts ✓ Solution to Quiz 3 (2:44) Download Video Subtitles & Transcripts ✓ Some Properties and Features of Fractals ✓ Video (11:22) Exploring the Koch curve Download Video Subtitles & Transcripts ✓ Quiz 1 ✓ Video (7:12) Exploring the Sierpiński triangle (and Quiz 1 solutions) Download Video Subtitles & Transcripts ✓ Video (6:54) Dimension and scaling Download Video Subtitles & Transcripts ✓ Quiz 2 ✓ Solution to Quiz 2 (3:24) Download Video Subtitles & Transcripts ✓ Video (5:41) Self-similar and scale-free Download Video Subtitles & Transcripts ✓ Video (4:06) Mathematical vs. real fractals Download Video Subtitles & Transcripts ✓ Exponent and Logarithm Review (Optional) ✓ Video (10:00) Exponent Properties Download Video Subtitles & Transcripts ✓ Quiz 1: Exponent Properties ✓ Quiz 2: More Exponent Properties ✓ Video (5:50) Logarithm definition Download Video Subtitles & Transcripts ✓ Quiz 3: Logarithm Basics ✓ Solution to Quiz 3 (5:00) Download Video Subtitles & Transcripts ✓ Video (5:40) Logarithm properties Download Video ✓ Quiz 4: Logarithm properties ✓ Solution to Quiz 4 (2:01) Download Video Subtitles & Transcripts ✓ Video (2:16) Using logarithms Download Video ✓ Quiz 5: Using logarithms ✓ Solution to Quiz 5 (4:55) Download Video ✓ Video (4:04) Logarithms: different bases Download Video ✓ Summary ✓ Video (8:37) Summary Download Video Subtitles & Transcripts Slides for this lecture ✓ Homework (Optional) ✓ Homework ✓ Homework solutions ✓ Test ✓ Test for Unit 1 Download Exam PDF ✓ Generating Fractals All Unit 2 Files Forum for Unit 2 ✓ Introduction ✓ Video (5:29) Introduction and elderberry fractals Download Video Subtitles & Transcripts ✓ Fractals via Deterministic Iteration ✓ Video (6:06) Koch curve via computer Download Video Subtitles & Transcripts ✓ Video (3:09) Irregular Koch curves Download Video Subtitles & Transcripts ✓ Explorations ✓ Video (2:49) "Solutions" to Explorations Download Video Subtitles & Transcripts ✓ Video (2:44) Quadratic Koch curve Download Video Subtitles & Transcripts ✓ Video (14:13) Iterated Function Systems and L-Systems Download Video Subtitles & Transcripts ✓ Adding a Bit of Randomness ✓ Video (9:29) The random Koch curve Download Video ✓ Quiz 1: Random Koch curve ✓ Video (7:50) Fractal landscapes Download Video ✓ The Chaos Game ✓ Video (7:52) Introducing the chaos game Download Video ✓ Video (5:28) Explaining the chaos game Download Video ✓ Video (4:28) Chaos game variations Download Video Subtitles & Transcripts ✓ Diffusion-Limited Aggregation ✓ Video (5:53) Introducing DLA Download Video ✓ Video (5:01) Experimenting with DLA Download Video Subtitles & Transcripts ✓ Video (2:28) More about DLA Download Video ✓ Summary ✓ Video (7:29) Unit 2 summary Download Video Slides for this lecture ✓ Programs and Resources ✓ Links to programs ✓ Other resources ✓ Homework (Optional) ✓ Homework ✓ Test ✓ No test for Unit 2 ✓ Box-Counting Dimension All Files for Unit 3 Forum for Unit 3 ✓ Introduction ✓ Video (4:27) Introduction Download Video Subtitles & Transcripts ✓ Basic Box-Counting ✓ Video (12:42) Box-counting: line and square Download Video ✓ Quiz 1 ✓ Video (4:30) Box-counting another line Download Video ✓ Video(8:50) Box counting the Sierpinski triangle Download Video ✓ Quiz 2: Box-counting the Cantor set ✓ Video (3:35) Box-counting and the Cantor set Download Video ✓ Box-Counting in Practice ✓ Video (8:39) Introduction: s must be small Download Video ✓ Video (15:08) Box-counting a circle Download Video ✓ Quiz 1: Box-counting the Koch curve ✓ Quiz 2: The dimension of the Koch curve ✓ Video (7:26) Log-log plots Download Video ✓ Video (11:31) Log-log plot for a square Download Video R code for making the log-log plot ✓ Quiz 3: Log-log plots ✓ Video (2:10) Solution to quiz 3 Download Video ✓ Video (11:03) Log-log plots: practicalities and issues Download Video ✓ Thinking about Dimensions ✓ Video (6:24) Dimensions and scaling Download Video Subtitles & Transcripts ✓ Video (3:55) What do dimensions tell us? Download Video ✓ Video (12:26) A tour through the dimensions Download Video ✓ Summary ✓ Video (10:28) Unit 3 Summary Download Video Slides for this lecture ✓ Homework (Optional) ✓ Homework ✓ Homework solutions ✓ Test ✓ Test for Unit 3 Download Exam PDF ✓ Introducing Power Laws All Unit 4 Files Forum for Unit 4 ✓ Introduction ✓ Video (1:49) Download Video Subtitles & Transcripts ✓ An Initial Example: Word Frequency ✓ Video (5:50) Weighing books Download Video Subtitles & Transcripts ✓ Video (9:41) Word frequencies Download Video Subtitles & Transcripts Slides for this lecture ✓ Video (6:44) A power law Download Video ✓ Quiz 1: Power-law practice ✓ Other Distributions ✓ Video (14:56) Central limit theorem Download Video ✓ Video (10:36) Exponential distributions Download Video ✓ Quiz 1: Exponential distribution ✓ Video (5:17) Discrete vs. continuous distributions Download Video ✓ Properties of Power Laws ✓ Video (13:39) Power laws are scale free Download Video ✓ Quiz 1: Power-law distribution practice ✓ Quiz 2: Exponential distribution practice ✓ Video (4:10) Solutions to quiz 1 and 2 Download Video ✓ Video (15:01) Only power laws are scale free (Optional) Download Video ✓ Video (7:18) Power laws have long tails Download Video ✓ When do Averages Exist? ✓ Video (10:40) The coin-toss game: A process with an average Download Video ✓ Quiz 1: The coin-toss game ✓ Video (17:12) A process without an average Download Video ✓ Video (9:28) Power laws and averages Download Video ✓ Interview: Nick Watkins ✓ Video (17:40) Interview: Nick Watkins Download Video ✓ Summary ✓ Video (14:50) Summary Download Video Slides for this lecture ✓ Homework (Optional) ✓ Homework ✓ Homework solutions ✓ Test ✓ Test for Unit 4 Download Exam PDF ✓ Coming soon... ✓ Power Laws in Empirical Data All Unit 5 Files Forum for Unit 5 ✓ Introduction ✓ Video (3:21) Introduction Download Video Subtitles & Transcripts ✓ Cumulative Distributions and Rank/Frequency Plots ✓ Video (5:07) Histograms and distributions Download Video Subtitles & Transcripts ✓ Video (10:16) Cumulative distributions Download Video ✓ Quiz 1: Cumulative Distribution Functions ✓ Quiz 2: Cumulative Distribution Functions ✓ Video (9:13) Rank/frequency plots Download Video ✓ Video (5:11) The exponent for the CDF (Optional) Download Video ✓ Video (9:50) Empirical examples of power-law CDFs Download Video ✓ Estimating the Exponent ✓ Video (13:08) The maximum likelihood estimator for alpha Download Video ✓ Video (5:22) Comparing the MLE with linear-fit methods Download Video ✓ Video (9:07) Estimating x_min (Optional) Download Video ✓ Video (11:42) Goodness of fit Download Video ✓ Other Long-tailed Distributions ✓ Video (10:03) Log-normal distributions Download Video ✓ Video (6:14) Choosing among alternatives (Optional) Download Video ✓ Video (7:32) Power-law or long-tailed? Download Video ✓ Summary ✓ Video (14:28) Summary Download Video Slides for this lecture ✓ Additional Resources ✓ Additional resources ✓ Homework (Optional) ✓ Homework ✓ Homework solutions ✓ Test ✓ Test for Unit 5 Download Exam PDF ✓ Generating Power Laws All Unit 6 Files Forum for Unit 6 ✓ Introduction ✓ Video (3:02) Introduction Download Video Subtitles & Transcripts ✓ Rich-get-Richer Models ✓ Video (5:18) Introducing the rich-get-richer idea Download Video Subtitles & Transcripts ✓ Video (13:16) A preferential attachment model Download Video ✓ Quiz 1: Preferential attachment ✓ Video (11:22) Further remarks on preferential attachment Download Video Subtitles & Transcripts ✓ Combinations of Exponentials ✓ Video (10:46) Combinations of exponentials Download Video ✓ Multiplicative Processes ✓ Video (9:24) Multiplicative processes produce log normals Download Video ✓ Video (6:02) Multiplicative processes produce power laws Download Video ✓ Optimization ✓ Video (9:12) Distribution networks Download Video ✓ Video (8:16) Highly optimized tolerance Download Video ✓ Video (4:12) Optimization and word frequency Download Video ✓ Video (6:02) General remarks on optimization Download Video ✓ Phase Transitions? ✓ Video (11:44) Percolation (Optional) Download Video ✓ Video (5:14) Universality (Optional) ✓ Video (7:36) How many power laws are from phase transitions? Download Video Subtitles & Transcripts ✓ Summary ✓ Video (3:51) What do power laws mean? Download Video ✓ Video (13.57) Unit 6 summary Download Video Slides for this lecture ✓ Homework (Optional) ✓ Homework for Unit 6 ✓ Homework solutions ✓ Additional Resources ✓ Additional resources ✓ Test ✓ Test for Unit 6 Download Exam PDF ✓ Metabolic Scaling All Unit 7 Files Forum for Unit 7 ✓ Introduction ✓ Video (9:37) Introduction and Kleiber's law Download Video Subtitles & Transcripts ✓ Metabolic Scaling ✓ Video (5:30) Review of basic scaling Download Video Subtitles & Transcripts ✓ Quiz 1: Scaling Practice ✓ Video (4:45) Metabolic scaling: is it linear? Download Video ✓ Video (6:17) How does surface area scale? Download Video ✓ Quiz 2: Metabolic scaling ✓ Video (6:12) Quiz 2 solution Download Video ✓ WBE Theory of Metabolic Scaling ✓ Video (15:37) Elements of the WBE theory Download Video ✓ Video (10:09) Other scaling relationships Download Video ✓ Quiz 1: More metabolic scaling ✓ Video (2:52) Quiz Solution Download Video ✓ Interview: Van Savage ✓ Video (15:46) Interview with Van Savage Download Video ✓ Interview: Geoffrey West ✓ Video (15:52) Interview with Geoffrey West Download Video Subtitles & Transcripts ✓ Summary ✓ Video (4:34) Remarks on trends vs. variation Download Video ✓ Video (8:53) Summary Download Video Slides for this lecture ✓ Additional Resources ✓ Additional resources ✓ Homework (Optional) ✓ Homework for Unit 7 ✓ Homework solutions ✓ Test ✓ Test for Unit 7 Download Exam PDF ✓ Urban Scaling All Unit 8 Files Forum for Unit 8 ✓ Introduction ✓ Introduction (2:31) Download Video Subtitles & Transcripts ✓ Empirical Results ✓ Video (7:19) Some initial results Download Video Subtitles & Transcripts ✓ Video (7:53) Patterns in the exponents Download Video Subtitles & Transcripts ✓ Quiz 1: Scaling Practice ✓ A Theory of Urban Scaling? ✓ Video (11:58) Toward a theory of urban scaling Download Video Subtitles & Transcripts ✓ Interview: Christa Brelsford ✓ Video (10:31) Interview: Christa Brelsford Download Video Subtitles & Transcripts ✓ Interview: Luis Bettencourt ✓ Video (17:22) Interview: Luís Bettencourt Download Video ✓ Summary ✓ Video (9:00) Reflections on urban scaling Download Video Subtitles & Transcripts ✓ Video (8:32) Summary Download Video Subtitles & Transcripts Slides for this lecture ✓ Homework (Optional) ✓ Homework for Unit 8 ✓ Homework solutions ✓ Test ✓ Test for Unit 8 Download Exam PDF ✓ Additional Resources ✓ Additional resources ✓ Conclusion and Summary All Unit 9 Files Forum for Unit 9 ✓ Summary ✓ Video (19:27) Summary of course Download Video Subtitles & Transcripts Slides for this lecture ✓ Farewell ✓ Video (2:50) Farewell Download Video Subtitles & Transcripts ✓ 3.2 Basic Box-Counting » Quiz 1 Quiz scores are NOT recorded. You may come back to quizzes and take them as many times as you like When you are finished, clicking the "Score" button at the bottom of the test will show you the correct responses.