Week 8 Response: Fractals

What interests me most this week was the topic of fractals discussed in lecture as well as in Wilson’s book. From lecture, fractals refer to “infinitely complex self-organizing, self-similar patterns in nature or image fragments or geometric shapes replicable and sub-dividable across different scales.” The specific thing that intrigues me the most about fractals is how they appear in many diverse areas, “from the complexity of natural phenomenon to the dynamic behavior of mathematical systems, and their striking beauty and wealth of detail has given them an immediate presence in our collective consciousness” (Wilson 331). Ron Eglash points out how our body is covered in fractals in his TED talk, “The fractals at the heart of African designs”. He told the audience to observe the bend between their thumbs and index pointers and how there are wrinkles within wrinkles… thus fitting the definition of a fractal.

For this week’s response, I will be curating a display of a few fractals on this post as well as comparing and contrasting each fractal.

1. Fractals in human lungs
Human lungs are another example of fractals within the human body. With this cast of the lungs, one can make out a tree shape (with each branching vein as a branch). The shared shape represents a concept in science known as the Structure-Function Relationship. The lungs and tree have similar shapes since that is the most ideal for each to serve their function: respiration.

2. Fractals in ice
The structure of a snowflake is actually based on fractals. Afterall there is a mathematical curve named the Koch snowflake which is described as a fractal curve. After each iteration of the recursion, the complexity increases within the shape formed by the Koch curve as well as the snowflake.

3. Fractals in flowers
Fractals allow flowers to take the shapes that they have. This is why flowers seem symmetrical and are made up of various layers. Fractals literally add another huge dimension to flowers as compared to other fractals mentioned above.

 

 

 

4. Fractals in electricity
A high voltage breakdown is captured within a 4″ block of acrylic. This is also similar to the structure of a tree; however, it does not share the same function. One can even see the shapes of mountains formed in the resulting structure.

 

The fractals all look different in some way and come from various aspects of life, but they are similar in the sense that they all have repetitive patterns to make them unique.

– Crystal Nguyen

Resources:
http://fractalfoundation.org/OFC/OFC-1-2.html
http://en.wikipedia.org/wiki/Koch_snowflake
http://fractalenlightenment.com/11944/photography/amazing-fractals-found-in-nature

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