Dorky Dork Dork.
So, not only did I just learn about Newton Basins (in concept, not practice), I'm posting about it! But I can't help it, because, damn it's cool.
It's like this: when you go to approximate the root of a complex number, you often come up with several solutions when using Newton's Method (again, concept, not application), so then that makes pretty patterns! Fractals of the simple sort. You guess a solution, and then you use the method over and over again to find the boundaries of each root range. :-)
Also neat: roots of negative numbers exist! I mean, in real life, beyond 'i'. They use them in "electronic circuits and ... biological models." Fun! It says to just think of it as a number that's 'not a distance.' hahaha!!! Yay!
Pics: http://aleph0.clarku.edu/~djoyce/newton/examples.html
Nerdy Reading: http://orion.math.iastate.edu/danwell/Fexplain/newt1.html
Ah, it's really the simple complex things that bring joy to life!
It's like this: when you go to approximate the root of a complex number, you often come up with several solutions when using Newton's Method (again, concept, not application), so then that makes pretty patterns! Fractals of the simple sort. You guess a solution, and then you use the method over and over again to find the boundaries of each root range. :-)
Also neat: roots of negative numbers exist! I mean, in real life, beyond 'i'. They use them in "electronic circuits and ... biological models." Fun! It says to just think of it as a number that's 'not a distance.' hahaha!!! Yay!
Pics: http://aleph0.clarku.edu/~djoyce/newton/examples.html
Nerdy Reading: http://orion.math.iastate.edu/danwell/Fexplain/newt1.html
Ah, it's really the simple complex things that bring joy to life!