How can starting with a guess and using Isaac Newton's iterative solving method to find the roots of polynomial equations produce fractals?
3Blue1Brown's Grant Sanderson explains in the following 26 minute video. That may sound like a lot, but it is one of the more visually captivating maths explainers we've come across in quite a while, which really takes off at about the halfway point when chaotic boundaries emerge.
Newton's method is also known as the Newton-Raphson method, which is one of the tools that make it possible to come up with approximate numerical solutions to equations where direct, exact solution aren't an option. Here's a nice written introduction to how the method works, where step one involves making your best guess at the answer!
Update 16 October 2021: The sequel, Where Newton meets Mandelbrot (or more fancifully, “holomorphic dynamics”), is out!
Labels: math
Welcome to the blogosphere's toolchest! Here, unlike other blogs dedicated to analyzing current events, we create easy-to-use, simple tools to do the math related to them so you can get in on the action too! If you would like to learn more about these tools, or if you would like to contribute ideas to develop for this blog, please e-mail us at:
ironman at politicalcalculations
Thanks in advance!
Closing values for previous trading day.
This site is primarily powered by:
CSS Validation
RSS Site Feed
JavaScript
The tools on this site are built using JavaScript. If you would like to learn more, one of the best free resources on the web is available at W3Schools.com.
Other Cool Resources
Blog Roll
