Complex Mapping Visualizer

#1

Post by vector_spaces » Fri, Mar 12, 2021, 11:53 PM UTC

Complex Mapping Visualizer
mabotkin.github.io

Re: Complex Mapping Visualizer

#2

Post by nabla9 » Sat, Mar 13, 2021, 1:31 PM UTC

This is really good learning aid. I hope I hand this when I was learning complex numbers.

1. draw a grid of horizontal and vertical lines,

2. then try

    z^X where x in 0.1, 0.5, 1, 1.1 ,1.5, 2

    1/z
    
    sin(X*z) where X in 0.1 ... 2

    1/sin(z)

3. ... and think and do the math (with pen and paper) until it makes sense.

4. can you figure out what 2^z is without trying out?

Re: Complex Mapping Visualizer

#3

Post by ianai » Sat, Mar 13, 2021, 2:34 PM UTC

Be sure to fudge with the range settings!

This one was fun: z^5+7z^4-3z^3-15z^2-z+9

Re: Complex Mapping Visualizer

#4

Post by bonzini » Sat, Mar 13, 2021, 3:03 PM UTC

This is a really cool technique, I programmed it on a graphing calculator back in my teens and it was perhaps the first thing I did that ended up on the web.

Re: Complex Mapping Visualizer

#5

Post by vincnetas » Sat, Mar 13, 2021, 3:12 PM UTC

Fork for ones to lazy to draw grid each time after reseting a mapping: https://vincnetas.github.io/complex-map/

Re: Complex Mapping Visualizer

#6

Post by jimkleiber » Sat, Mar 13, 2021, 6:12 PM UTC

ianai wrote: post #3

Be sure to fudge with the range settings! This one was fun: z^5+7z^4-3z^3-15z^2-z+9

Hmm, when I try that one it gives me an "invalid function" dialog. Tried it on Firefox and Chrome.

Any suggestion on how to get it work? Do I have to change the range settings, if so, to what?

Re: Complex Mapping Visualizer

#7

Post by brandonpelfrey » Sat, Mar 13, 2021, 7:26 PM UTC

If you like this kind of stuff, also feel free to play around with a realtime complex-valued expression->glsl version I made a while back. I like the one here a lot as well since it probably runs everywhere even without webgl

http://brandonpelfrey.github.io/complex-function-plot/?expre...

Re: Complex Mapping Visualizer

#8

Post by ianai » Sun, Mar 14, 2021, 1:24 PM UTC

jimkleiber wrote: post #6

ianai wrote: post #3

Be sure to fudge with the range settings! This one was fun: z^5+7z^4-3z^3-15z^2-z+9

Hmm, when I try that one it gives me an "invalid function" dialog. Tried it on Firefox and Chrome. Any suggestion on how to get it work? Do I have to change the range settings, if so, to what?

I think I multiplied the W range settings by 10?