Winding numbers and domain coloring

An algorithm for numerically solving certain 2d equations. Help fund future projects:   / 3blue1brown   An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/winding-thanks Writing and animations by Sridhar Ramesh, with editing and narration by Grant Sanderson. Even though we described how winding numbers can be used to solve 2d equations at a high level, it's worth pointing out that there are a few details missing for if you wanted to actually implement this. For example, in order to determine how often to sample points, you'd want to have some bounds on the rate at which the direction of the output changes. We will perhaps discuss this more in a follow-on video! Music by Vincent Rubinetti: https://vincerubinetti.bandcamp.com/a... ------------------ 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, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter:   / 3blue1brown   Patreon:   / 3blue1brown   Facebook:   / 3blue1brown   Reddit:   / 3blue1brown