CK-12 Geometry-Concepts

7.13. Self-Similarity http://www.ck12.org

7.13 Self-Similarity

Here you’ll learn what it means for an object to be self-similar and you’ll be introduced to some common examples
of self-similarity.

What if you were given an object, like a triangle or a snowflake, in which a part of it could be enlarged (or shrunk)
to look like the whole object? What would each successive iteration of that object look like? After completing this
Concept, you’ll be able to use the idea of self-similarity to answer questions like this one.

Watch This

MEDIA

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URL: http://www.ck12.org/flx/render/embeddedobject/52552

CK-12 Foundation: Chapter7SelfSimilarityA

MEDIA

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URL: http://www.ck12.org/flx/render/embeddedobject/10317

Brain Waves: Sierpinski Triangle

Guidance

When one part of an object can be enlarged (or shrunk) to look like the whole object it isself-similar.

To explore self-similarity, we will go through some examples. Typically, each step of a process is called aniteration.
The first level is calledStage 0.

Example A (Sierpinski Triangle)

The Sierpinski triangle iterates a triangle by connecting the midpoints of the sides and shading the central triangle
(Stage 1). Repeat this process for the unshaded triangles in Stage 1 to get Stage 2.