<video><title>Fractopia: 2. Fractals in Nature</title><description>Join Sebastian Schepis in a fascinating exploration of fractals - their history, their presence in our arts, architecture, bodies, and environment. We'll also explore how fractals are used in technology, examining the use of fractals in compression, machine learning and much more.</description><transcript><transcript><line from="00:00:00,000" to="00:00:10,000">Welcome back fellow fractal explorers. In our last episode, we introduced the basics of fractal geometry and its discovery by pioneering minds like mandal brought.</line><line from="00:00:10,000" to="00:00:22,000">We learned about the hallmarks of fractals like self-similarity, fractional dimensions, and infinite complexity. Today we're going to venture out into the natural world.</line><line from="00:00:22,000" to="00:00:29,000">To witness, first hand the abundance of fractal patterns in living systems and landscapes across scales.</line><line from="00:00:29,000" to="00:00:37,000">From the branching angles of trees to the rhythm of our heartbeats, we'll see signatures of fractal geometry everywhere.</line><line from="00:00:37,000" to="00:00:46,000">Nature leverages these fractal shapes for vital functions like maximizing surface area, optimizing networks, and generating endless diversity.</line><line from="00:00:47,000" to="00:00:53,000">Fractals reflect the way organic processes utilize recursion and feedback to build complexity,</line><line from="00:00:53,000" to="00:00:59,000">understanding these natural fractal forms teaches us about life's intricate dances,</line><line from="00:00:59,000" to="00:01:06,000">and mathematically modeling them helps us recreate realistic structures to get ready to zoom in on broccoli,</line><line from="00:01:06,000" to="00:01:13,000">soar over mountain ranges, and dive deep into your own fractal physiology.</line><line from="00:01:14,000" to="00:01:23,000">Let's explore why fractals fill the forests, and flow through our vein. Our first stop on the natural fractals tour is the ragged edge,</line><line from="00:01:23,000" to="00:01:32,000">where land meets water, the fractal coastline. In the 1960s, Benoit Mandelbrot analyzed the contours of Britain,</line><line from="00:01:32,000" to="00:01:40,000">and found that the coastline length depends on the scale of measurement, use a mile long ruler, and you'll measure one length,</line><line from="00:01:40,000" to="00:01:46,000">use a yardstick, and the length is longer due to detecting more twists, and turn.</line><line from="00:01:46,000" to="00:01:51,000">This statistical self-similarity results from the coast carving through complex landscapes,</line><line from="00:01:51,000" to="00:01:59,000">with bays, cliffs, and inlets forming across scales. Mandelbrot proposed that coastlines have fractional dimensions,</line><line from="00:01:59,000" to="00:02:06,000">reflecting this, similar fractal geometry appears in the branching shapes of rivers and tributaries,</line><line from="00:02:06,000" to="00:02:14,000">just as magnification alters measured coasts, so too for rivers as smaller rivulets appear under a microscope.</line><line from="00:02:14,000" to="00:02:19,000">Nature's edges elegantly display fractal contour, beyond the ocean's edge,</line><line from="00:02:19,000" to="00:02:25,000">fractal patterns also abound in landscapes, from the curves of rolling hills to craggy mountain peaks.</line><line from="00:02:25,000" to="00:02:32,000">Mathematically, the roughness of mountain skylines can be modeled using fractional brownie and motion,</line><line from="00:02:32,000" to="00:02:38,000">a stochastic process that generates statistically self-similar fractal terrain.</line><line from="00:02:38,000" to="00:02:45,000">This technique can realistically simulate mountains, cliffs, and other natural landforms, in aerial views,</line><line from="00:02:45,000" to="00:02:49,000">the branching streams and tributaries of river networks.</line><line from="00:02:49,000" to="00:02:56,000">Snake across the land, in fractal dendritic patterns, to efficiently carve out the terrain.</line><line from="00:02:56,000" to="00:03:01,000">The self-similar splitting allows covering area while minimizing channel lengths.</line><line from="00:03:01,000" to="00:03:10,000">Geometry also appears in wind-blown sand dunes, where the roughness behaves statistically similar across scales,</line><line from="00:03:10,000" to="00:03:18,000">and in the puffy geometry of clouds, which have fractal boundaries from turbulent air currents mixing moisture,</line><line from="00:03:18,000" to="00:03:25,000">clearly the forces shaping our planet's surface, erosion, fluids, gravity, wind,</line><line from="00:03:26,000" to="00:03:29,000">Generate repetitive patterns across scales.</line><line from="00:03:29,000" to="00:03:34,000">Fractals reflect nature's recurring handiwork and sculpting landscapes beyond the landscape,</line><line from="00:03:34,000" to="00:03:38,000">the other dominant visible structures in nature, plants and trees.</line><line from="00:03:38,000" to="00:03:44,000">Here too, fractal patterns abound due to efficient growth algorithms evolved over eons.</line><line from="00:03:44,000" to="00:03:51,000">The branching architecture of trees and leaves optimizes light harvesting and structural integrity to recursive fractal splitting.</line><line from="00:03:52,000" to="00:03:59,000">Models reproduce these natural patterns using L systems, which apply repeating rules to generate self-similar branching shape.</line><line from="00:03:59,000" to="00:04:07,000">In ferns, the placement of leaflets on the ratches mirrors the pattern of fronds branching off the resum underground.</line><line from="00:04:07,000" to="00:04:13,000">This self-referencing geometry gets reflected above and below ground, the spiraling florets,</line><line from="00:04:13,000" to="00:04:21,000">of rominesco broccoli, and cauliflower demonstrate dazzling fractal arrangements to maximize space filling.</line><line from="00:04:21,000" to="00:04:29,000">Their conical repetitions illustrate the exact self-similarity, plants leverage fractal shapes in clever ways.</line><line from="00:04:29,000" to="00:04:40,000">To replicate structural motifs across scales, pack more productivity into finite space using fractal branching and build recursive patterns to fill areas.</line><line from="00:04:40,000" to="00:04:47,000">Fractals offer tested blueprints for optimal organic growth, zooming into the wonders of the human body.</line><line from="00:04:47,000" to="00:04:55,000">We find fractal geometries underlying our very anatomy, from the airways in our lungs to the networks of our nerves.</line><line from="00:04:55,000" to="00:05:04,000">The bronchial tree that branches through our lungs does so in a fractal pattern to maximize surface area for oxygen absorption.</line><line from="00:05:04,000" to="00:05:10,000">This respiratory tree actually divides over 20 generations down to the alveoli.</line><line from="00:05:10,000" to="00:05:21,000">Our circulatory system forms a fractal network to efficiently distribute blood by branching arteries into smaller capillaries, then back in domains.</line><line from="00:05:21,000" to="00:05:30,000">The flow through this vasculature is turbulent and exhibits fractal dynamic, even our heart beats fluctuate in a fractal manner.</line><line from="00:05:31,000" to="00:05:47,000">The intervals between beats show self-similar patterns across time scales described by a fractal dimension from organ systems down to tissues and cellular processes, fractal scaling laws, enable efficient performance.</line><line from="00:05:47,000" to="00:05:59,000">Our bodies contain fractal signatures of help beyond plants and people, fractal formations permeate the rest of the animal kingdom and natural world, showing nature's endless creativity.</line><line from="00:05:59,000" to="00:06:05,000">In mollusks, the excess skeleton displays fractal grooves that increase strength in surface area.</line><line from="00:06:05,000" to="00:06:15,000">In coral reefs, the fractal branching maximizes habitat, the dragonflies wing contains fractal patterns that improve aerodynamics.</line><line from="00:06:16,000" to="00:06:19,000">See horses have anatomies full of squares spirals.</line><line from="00:06:19,000" to="00:06:32,000">In nest building by birds, bees and termites, the recursive architectural patterns create stable, insulating homes using simple behavioral rules.</line><line from="00:06:32,000" to="00:06:41,000">When ants follow firm own trails and bees traverse flower patches, their flight patterns show fractal properties to efficiently find resources.</line><line from="00:06:41,000" to="00:06:51,000">Across ecosystems, fractal networks appear in predator prey dynamics, population distributions, and energy transfers.</line><line from="00:06:51,000" to="00:07:05,000">Crackles reflect nature's propensity for self-organized complexity, wherever we look in the natural world, fractal shapes and networks, enhance life through simple recursive rules, generating beautiful complex.</line><line from="00:07:05,000" to="00:07:15,000">As we've seen, fractal patterns truly are everywhere in the natural world, from coastlines to mountain ranges, plants and physiology, animals and ecosystems.</line><line from="00:07:15,000" to="00:07:26,000">Nature is full of self-similarity across scales, fractal geometry reflects life's innate tendency to build complexity through simple recursive rules and feedback processes.</line><line from="00:07:26,000" to="00:07:32,000">These shapes optimize growth, enhance function, and create diversity.</line><line from="00:07:32,000" to="00:07:42,000">Studying and modeling natural fractals mathematically is helping us better understand living systems and recreate realistic structures in computer graphics and engineering.</line><line from="00:07:42,000" to="00:07:59,000">In our next episode, we'll explore some of the mathematical techniques used to intentionally construct different fractal shapes for insights into their infinite complexity, until then keep noticing fractals when your outdoors among the trees and clouds.</line><line from="00:07:59,000" to="00:08:10,000">I appreciate that your own body contains these beautiful repeating patterns, evolve for optimal health, and ponder how mundane rules can be get such marvelous complexity.</line></transcript></transcript></video>