1.6 Power Laws, Scale Invariance, and Diversity - World Science U

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1.6 Power Laws, Scale Invariance, and Diversity

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1.6 Power Laws, Scale Invariance, and Diversity

Question 1 of 2

1. Question
What is scale invariance and how is it related to self-similarity? Scale invariance is...
- 1. … when an object cannot be scaled without using the power law. It is self-similar, because after scaling, it can be turned back into its original by squaring.
- 2. … when regardless of the size of an object the same principle (e.g., proportion) will hold. It is self-similar, because after scaling, it can be turned back into its original by applying the power law.
- 3. … when an object's proportions vary with size. It is self-similar, because after scaling it still looks roughly the same.
- 4. ... when an object’s proportions vary with size according to the power law. It is self-similar, because it cannot be turned back into its original form without changing proportions.
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Question 2 of 2

2. Question
What is an example of Allometric and Isometric scaling?
- 1. Allometric: Urinary System and Isometric: Skeletal Structure in Vertebrates
- 2. Allometric: Urinary System and Isometric: Brain Size Relative to Body Size
- 3. Allometric: Brain Size Relative to Body Size and Isometric: Skeletal Structure in Vertebrates
- 4. Allometric: Skeletal Structure in Vertebrates and Isometric: Urinary System
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