Fractals: a world in a grain of sand | Ben Weiss | TEDxVeniceBeach
TEDx Talks・13 minutes read
William Blake's verse on patterns in nature relates to fractals discovered later; Benoit Mandelbrot simplified fractal analysis with an equation, leading to chaos theory and fractal geometry, showcasing infinite complexity and self-similarity in the Mandelbrot set and inspiring exploration through an app for artistic and therapeutic purposes, reflecting human consciousness.
Insights
- William Blake's verse from 200 years ago about patterns in nature foreshadowed the discovery of fractals, which are repeating patterns found in various natural phenomena like galaxies and human biology, showcasing self-similarity at different scales.
- Benoit Mandelbrot's groundbreaking work simplified the analysis of fractals with a basic equation, leading to the development of chaos theory and fractal geometry, demonstrating how seemingly complex shapes can be understood through mathematical principles, inspiring new ways of exploring art, science, and human cognition.
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Recent questions
What are fractals?
Fractals are repeating patterns at different scales.
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Summary
00:00
"Fractals: Nature's Patterns Unveiled Through Math"
- William Blake wrote a verse 200 years ago about seeing patterns in nature, which can be related to fractals discovered 170 years later.
- Fractals are patterns that repeat at different scales, seen in galaxies, weather patterns, and human biology like lungs and circulatory systems.
- Fractals were initially considered too complex to analyze mathematically due to their unique shapes.
- Benoit Mandelbrot simplified the understanding of fractals with a simple equation, leading to the development of chaos theory and fractal geometry.
- The Mandelbrot set, generated from a simple formula, showcases infinite complexity and self-similarity.
- Advancements in computing power have allowed for real-time exploration of the Mandelbrot set on cell phones.
- Fractal images can be enhanced with color, shading, lighting, and texture, revealing hidden patterns in the math.
- An app was developed to interactively explore fractals without intimidating math equations, aiming to inspire interest in mathematics.
- The app allows users to manipulate colors, lighting, and textures of fractals, creating an immersive and artistic experience.
- Fractals, with their intricate patterns, may have a similar effect on the brain as psychedelic experiences, potentially offering therapeutic benefits for conditions like PTSD and depression.
13:57
The Mind: A Fractal Engine of Complexity
- The brain may not be a fractal, but it serves as a powerful engine for generating fractal levels of complexity, suggesting that the mind could be fractal; fractal images resonate deeply with us, potentially reflecting ourselves and offering insights into human perception and consciousness, inspiring further understanding of complex concepts through simplicity.
