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#newton'sfractal#fractals#root-finding

Newton’s fractal (which Newton knew nothing about)

3Blue1Brown

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Beginner. No background in the topic needed.

3.2M views5 years ago1 recommendation

Computer scienceGraphics and audioMath for programmersRendering

Grant Sanderson explains the mathematics and visual complexity behind Newton's fractal and root-finding algorithms.

Who knew root-finding could be so complicated? Next part: youtu.be/LqbZpur38nw Special thanks to the following supporters: 3b1b.co/lessons/newtons-fractal#thanks An equally valuable form of support is to simply share the videos. Thanks to these viewers for their contributions to translations German: Luatic Hebrew: Omer Tuchfeld Portuguese: luiz12apn ------------------ Interactive for this video: 3blue1brown.com/lessons/newtons-fractal On fractal dimension: youtu.be/gB9n2gHsHN4 Mathologer on the cubic formula: youtu.be/N-KXStupwsc Some articles on Newton's Fractal, and its cousins: chiark.greenend.org.uk/~sgtatham/newton/ blbadger.github.io/polynomial-roots.html Some of the videos from this year's Summer of Math Exposition are fairly relevant to the topics covered here. Take a look at these ones, The Beauty of Bézier Curves youtu.be/aVwxzDHniEw The insolubility of the quintic: youtu.be/BSHv9Elk1MU The math behind rasterizing fonts: youtu.be/LaYPoMPRSlk Viewer-made interactive: codepen.io/mherreshoff/full/RwZPazd --- These animations are largely made using a custom python library, manim. See the FAQ comments here: 3blue1brown.com/faq#manim github.com/3b1b/manim github.com/ManimCommunity/manim/ You can find code for specific videos and projects here: github.com/3b1b/videos/ Music by Vincent Rubinetti. vincentrubinetti.com/ Download the music on Bandcamp: vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown Stream the music on Spotify: open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u ------------------ Timestamps: - Intro - Roots of polynomials - Newton’s method - The fractal - The boundary property - Closing thoughts ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe: 3b1b.co/subscribe Various social media stuffs: Website: 3blue1brown.com Twitter: twitter.com/3blue1brown Reddit: reddit.com/r/3blue1brown Instagram: instagram.com/3blue1brown_animations/ Patreon: patreon.com/3blue1brown Facebook: facebook.com/3blue1brown

Why it's here

1 person recommends this

What people say. Inspired a developer to build a high-performance fractal rendering demo comparing JavaScript and Rust WebAssembly.

u/verdurLLCin r/rust • Recommends

On “[Media] I made a website to demonstrate performance difference in fractal rendering with JS, rust-wasm, rust-wasm + SIMDs, rust-wasm + SIMDs + multithreading”

Hi everybody! This is a demo project that I made trying to achieve maximum image processing performance using only CPU. # \>> Live demo here << There you can select different drawing techniques, count of used threads and fractal's iterations count. The rendered fractal is Newton's fractal. I chose it inspired by 3blue1brown's video about these fractals. I'm still newbie in rust, so my code can be bad. Source link: https://github.com/alordash/newton-fractal P.S. Huge thanks to people in rust community discord server who helped me!
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