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Fractal Geometry and Trees – Katherine Loop

Fractal Branching

Photo credit: Ignacio Sanz via Visual hunt / CC BY-SA

Look closely at the picture of a tree’s branches. Notice how a pattern continues to repeat itself. The large branches break off into smaller ones that divide into smaller ones and smaller ones still.

Did you realize that math helps us describe this branching of trees? Well, it does! Fractal geometry is used to describe many aspects of creation, including the branching of trees. In fact, fractal geometry can be used to mathematically model creation (such as when designing a computer-generated backdrop for a movie).

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Without going into the details or a technical definition, “a fractal is a never ending pattern that repeats itself at different scales.”[1] In the case of the tree, there’s a pattern of branches dividing into further branches that repeats itself over and over again.

As you watch the leaves fall this year and notice the branching structure left visible, know that math helps us describe the orderly way God causes trees to grow. Don’t let the details and rules in math fool you—math is a “tool” we can use to explore His creation. It’s complex (and there are so many different “branches” of it) because God created a complex universe that takes many different “tools” to even attempt to model and describe.

Note: If you’d like a non-technical look at fractals, here’s a fairly simple overview.

Revealing ArithmeticWant help showing your children how math is a useful tool? Revealing Arithmetic is a guide you can use alongside any curriculum to help you teach math from a biblical worldview.

“Revealing Arithmetic is the perfect reference work to assist homeschoolers teaching math to students of all ages. Whatever curriculum you are using, this book explains math concepts in clear, easy-to-understand principles from the Word of God…After reading Revealing Arithmetic for myself, I spent several weeks reading the chapters aloud with my children. We were awed by Gods sovereignty over all of creation; His constancy that sustains all of the principles we use each day; and our complete dependence on Him each moment.”- From a review by Lea Ann Garfias, Homeschool Mom and author of the blog “Whatever State I Am”

Check it out.


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Written by Kate [Loop] Hannon

After having her own view of math transformed, Katherine has been researching, writing, and speaking on a biblical worldview of math for more than a decade. She's the author of the popular Principles math curriculum series published by Master Books. Her books on math and a biblical worldview have been used by individuals, homeschool groups, and Christian schools and colleges. Receive a free video on transforming math at

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