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Self-Similarity Dimension
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Welcome and Overview
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Some Properties and Features of Fractals
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Exponent and Logarithm Review (Optional)
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Video (10:00) Exponent Properties
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Quiz 1: Exponent Properties
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Quiz 2: More Exponent Properties
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Video (5:50) Logarithm definition
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Quiz 3: Logarithm Basics
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Solution to Quiz 3 (5:00)
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Video (5:40) Logarithm properties
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Quiz 4: Logarithm properties
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Solution to Quiz 4 (2:01)
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Video (2:16) Using logarithms
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Quiz 5: Using logarithms
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Solution to Quiz 5 (4:55)
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Video (4:04) Logarithms: different bases
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Summary
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Homework (Optional)
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Introduction
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Fractals via Deterministic Iteration
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Adding a Bit of Randomness
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The Chaos Game
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Diffusion-Limited Aggregation
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Summary
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Programs and Resources
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Homework (Optional)
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Test
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Introduction
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Basic Box-Counting
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Box-Counting in Practice
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Video (8:39) Introduction: s must be small
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Video (15:08) Box-counting a circle
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Quiz 1: Box-counting the Koch curve
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Quiz 2: The dimension of the Koch curve
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Video (7:26) Log-log plots
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Video (11:31) Log-log plot for a square
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Quiz 3: Log-log plots
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Video (2:10) Solution to quiz 3
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Video (11:03) Log-log plots: practicalities and issues
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Thinking about Dimensions
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Summary
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Homework (Optional)
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Test
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Introduction
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An Initial Example: Word Frequency
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Other Distributions
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Properties of Power Laws
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When do Averages Exist?
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Interview: Nick Watkins
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Summary
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Homework (Optional)
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Test
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Introduction
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Cumulative Distributions and Rank/Frequency Plots
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Estimating the Exponent
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Other Long-tailed Distributions
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Summary
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Additional Resources
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Homework (Optional)
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Test
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Introduction
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Rich-get-Richer Models
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Combinations of Exponentials
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Multiplicative Processes
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Optimization
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Phase Transitions?
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Homework (Optional)
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Additional Resources
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Test
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Introduction
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Metabolic Scaling
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WBE Theory of Metabolic Scaling
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Interview: Van Savage
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Interview: Geoffrey West
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Additional Resources
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Homework (Optional)
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Test
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Introduction
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Empirical Results
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A Theory of Urban Scaling?
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Interview: Christa Brelsford
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Interview: Luis Bettencourt
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Test
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Homework (Optional)
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Additional Resources
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Summary
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Farewell
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8.9 Additional Resources » Additional resources
Papers
Bettencourt, Luis, and Geoffrey West. "A unified theory of urban living." Nature. 467.7318 (2010): 912-913. [pdf] A short, non-technical essay about the potential impacts of urban scaling research.
Bettencourt, Luís MA, et al. "Growth, innovation, scaling, and the pace of life in cities." Proceedings of the national academy of sciences 104.17 (2007): 7301-7306. [html] One of the first papers to apply ideas from metabolic scaling to cities.
Videos
Luís Bettencourt, From Scaling to Practice: Real World Applications of Cities Research . Santa Fe Institute Science Board Symposium. May 12, 2014.
Luís Bettencourt, Cities as complex adaptative systems. A talk given at the Centro de Investigaciones Interdisciplinarias en Ciencias y Humanidads, Universidad Nacional Autónoma de México, November, 2013.
Geoffrey West, The Surprising Math of Cities and Corporations. a TED talk from July 2011.
See also the page for the Cities, scaling, and sustainability group at the Santa Fe Institute.