Finite subdivision rule

High school (ages 12+)
Mathematics & Numbers

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Step 1 · Read the article

Open the article and read it at the level above. Then answer the questions below in your own words.

https://smallwhale.org/articles/finite-subdivision-rule

Write what each word means, using the article.

Do not copy the article. Write two things you learned, the way you would explain them to a friend.

Answers below are taken from the article’s stored facts, so they match what the student read.

1. What is the generative principle?Enables the creation of complex, often non-self-similar patterns with controlled variations
2. What is the architectural design?Informs the creation of intricate facades, tessellations, and structural elements
3. How is a finite subdivision rule different from a fractal?A fractal repeats the exact same shape at every level, while a finite subdivision rule can change the shapes a little each time.
4. Why is it called "finite"?Because the cutting stops after a set number of steps, giving a finished shape instead of going on forever.

Recursive Decomposition: Breaking down a shape into smaller versions of itself, applied repeatedly.
Self-Similarity: The property of a shape looking the same at different scales of magnification.
Substitution Tiling: A tiling where each tile can be replaced by a specific arrangement of smaller tiles.
Hyperbolic Geometry: A type of non-Euclidean geometry where the sum of angles in a triangle is less than 180 degrees.