Watch Current Video List All Videos ✓ Introduction to Fractals and Dimension All Unit 1 Files Unit 1 Forum ✓ 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 Unit 2 Forum ✓ 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 Unit 3 Forum ✓ 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 Unit 4 Forum ✓ 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 ✓ Power Laws in Empirical Data All Unit 5 Files Unit 5 Forum ✓ 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 Unit 6 Forum ✓ 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 Unit 7 Forum ✓ 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 Unit 8 Forum ✓ 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 ✓ Test ✓ Test for Unit 8 Download Exam PDF ✓ Homework (Optional) ✓ Homework for Unit 8 ✓ Homework solutions ✓ Additional Resources ✓ Additional resources ✓ Conclusion and Summary All Unit 9 Files Unit 9 Forum ✓ Summary ✓ Video (19:27) Summary of course Download Video Subtitles & Transcripts Slides for this lecture ✓ Farewell ✓ Video (2:50) Farewell Download Video Subtitles & Transcripts ✓ 6.5 Optimization » Video (9:12) Distribution networks Download Video