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What are fractal patterns?
Chaotic equations that form complex patterns that increase with magnification are known as fractals.
What is the most famous fractal?
The Mandelbrot set introduced by John Briggs is known to be the most famous fractal in modern mathematics, mainly because of its haunting beauty.
Where do you find fractals?
The world is full of complicated patterns called fractals. From the tiny, little patterns of seashells to the magnificent wonder of galaxies, they can be found in nature quite easily.
How are fractals used in real life?
Fractals are used to detect and capture the complexity of various structures. They are also used to analyze bacterial patterns and other biological processes.
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Psychedelic fractals incoming!
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Neurons in the human cortex display fractal patterns in the branching of brain cells.
Lungs use the large surface area resulting from the branching patterns to exchange oxygen.
Trees display fractal branching patterns.
Coastlines are among the first fractals studied.
Clouds display repeated fractal patterns.
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Are fractals viewed in our reality (4 Dimensions) smooth in shape in other realities (additional dimensions)?
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One of the coolest natural occurring phenomena in nature and math.
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I fuckin’ hated these things in math classes because they were usually some ridiculous problem, but the Mandelbrot set is pretty cool.
Give me the Fibonacci sequence all day long though.
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Not exactly true. Fractals are hierarchically self-similar as their main common trait, but only a portion of them are generated by chaotic equations or exhibit chaotic behavior.
The Hilbert curve, for example, is an entirely non-chaotic fractal, while Lyapunov fractals (chaotic equations and behaviors) and the Mandelbrot set (deterministic iterative equations but chaotic behaviors) could be considered chaotic or a mix in-between.
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I’m getting PTSD…
lol, this is the best
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Is rhis the shibanacci sequence?
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I know fractals aint never done nothing for me professionally. Probably i am two dumbs for it
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Follow the science!
Or math…
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Yeah but it’s not really either/or. A lot of the Fibonacci photos you shared exhibit not only the golden ratio and so on but also fractal features and other interesting nature-math links like rotational symmetry.
Chemist Istvan Hargittai took a break from his usually dense works to create a beautiful 200-page photobook of these types of forms/structures found both in nature and manmade objects. It’s called “Visual Symmetry” for anyone interested:
I think the Fibonnaci sequence shows up more in surprising us with the hidden order in visual forms (and is many times questionably applied to photos IMHO). What underlies it often is a basic result of natural processes like meristem cell cluster packing in flowering plants. In other words, it really could be no other way, although I suppose alternate worlds are possible. That such a simple sequence describes the “way that things are” for a lot of natural phenomena is definitely an astounding mathematical fact.
Fractals also desribe visual forms (like the broccoli in OP’s video) but also describe non-visual processes and structures (including, of all things, human psychology). Together with chaos theory, they reveal hidden orders in the strangest of patterns, like for example the chaoscopy discovery that the aperiodic timings between drops of water from a leaky faucet are actually a chaotic time series that plots as a smooth curve.
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But have you ever looked at a fractal…
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