The idea of infinity seems distant. However, we live in a world created by an infinite God, and if you look closely enough, little fragments of His infinite nature are replicated in the patterns of the finite nature we live in. One of the most concrete, and perhaps beautiful, examples of this is found in fractals. Fractals are infinitely repeating geometric patterns, in which each repetition of the pattern is the original pattern on a smaller scale, namely, they are self-similar.
The best way to understand fractals is to look at them. One of the most famous examples of fractals is the Mandelbrot Set, a set of numbers, which, when plotted, results in a fractal pattern along the edges (or boundaries). As can be seen, the edges are smaller images of the initial shape, and the edges of the edges are even smaller images of the initial shape, and the edges of the edge’s edges are even smaller images of the initial shape, a pattern that continues forever.
Actually, this might be a bad first example of a fractal, as these patterns upon patterns become intensely complex as you zoom closer and closer in on the edges, as can be seen in this image of the same fractal:
This same infinite intricacy is present in even the most common objects in nature, for example, trees. The tree itself is the initial pattern, and then the branches are miniature versions of the tree, and then the branches have smaller versions of themselves, and then those branches branch off into smaller twig versions of themselves. Even the roots follow the same pattern, branching out and out into smaller and smaller versions. And branching pervades all of nature– not just trees. Rivers have fractal branches, blood vessels have fractal branches, snowflakes have fractal branches, and so do kidneys, crystals, galaxies– the list extends on and on.
However, it should be impossible for nature to organize itself so neatly! The second law of thermodynamics states that the entropy– or disorder– of a system when left to its own devices will only increase! (That’s why bedrooms get messy effortlessly, but they don’t clean themselves.) Why then does nature fold itself into elegant patterns?
These fractal patterns are actually the result of chaos, not order. Even hurricanes and avalanches, the epitomes of chaos end up following fractal patterns. This is partly because dynamic systems are always hitting new boundaries, which then have their own boundaries, which also have their own boundaries. It’s the same branching on branching that’s found in calmer systems like tree roots and snowflakes. For example, imagine you stacked one million grains of sand on top of each other and then watched the sand avalanche downwards. The resulting sandpile could be modeled by this simulation created by three physicists in 1987, in which dark blue pixels represent no sand grains, light blue pixels represent one grain, yellow represents a stack of two, and red represents a stack of three.
And if you put a billion grains of sand on the center dot, it would look like this:
Again, fractals! Nature is lazy– it wants to be in the state where it’s expending the least amount of energy. The sand particles want to find this restful state– this equilibrium– and the line between motion and rest ends up being the wiggly fractal line that crops up again and again and again. Of course, these fractals in nature aren’t as immaculate as they are in carefully programmed simulations as there are outside obstructions that interrupt the infinite spiraling of these patterns, not to mention that perfect sandpiles don’t exist. But this is where disorder would organize itself if it could. In other words, the disorder of the universe can be modeled by organized patterns, reflecting God’s infinitely organized mind found at the core of the universe’s design.
Sources:
Ellenberg, Jordan. “The Math of the Amazing Sandpile.” Nautilus, 6 October 2021. https://nautil.us/issue/107/the-edge/the-math-of-the-amazing-sandpile?utm_source=pocket-newtab.
Pearce, Kyle. “Fractals in Nature: Develop Your Pattern Recognition Skills in the Forest.” DIYGenius, 4 November 2018. https://www.diygenius.com/fractals-in-nature/.
Fractals TV. “Fractals– Hunting the Hidden Dimension.” YouTube, 23 September 2017. https://www.youtube.com/watch?v=FKttSB4pzug.
Image Sources:
https://www.energy.gov/sites/default/files/styles/full_article_width/public/snowflake.png?itok=osZ50pCF
https://upload.wikimedia.org/wikipedia/commons/a/a4/Mandel_zoom_11_satellite_double_spiral.jpg
https://treecaretips.org/wp-content/uploads/2020/06/photo-of-old-tree-1792626-scaled.jpg
