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
Click image to the left for more content.CK-12 Foundation: Chapter7SelfSimilarityA
MEDIA
Click image to the left for more content.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.
Example B (Fractals)
Like the Sierpinski triangle, a fractal is another self-similar object that is repeated at smaller scales. Below are the
first three stages of the Koch snowflake.