If you have found yourself thinking, “My day has been nice thus far, but has been missing an excellent explanation of the foundations of imaginary number theory” then have I got something for you! This link. Also it has a fractal and those are always fun.
Interesting. I stumbled across something similar to this regarding the Mandelbrot set and probably the more visual Julia Set. Complex number theory is one heck of a mind bender to completely understand, but the simplicity within the Mandelbrot set is actually in its 2-D structure. It really is something else to see such imagery with all of its repetitiveness created with a rather simple formula (multiplied, or iterated a gazillion or so times). If you really want to get your inner geek on, take a look at the 3-D monster called the Mandelbulb. That is in a league of its own.
Very cool! It's been a while since I delved into i^2…
Oh jchem, the Mandelbulb just made my day!
The mandelbulb made me do some searching and led me to forums about all sorts of 3D fractal sets, some of them much more like architecture, which gave me the idea (something that I see a commenter for the mandelbulb set thought of too) to put it in a 3D printer to make a tangible object.
The imaginary number bit reminded me of the old “cork in water” problem, where e^x was solution, but x could be complex, which turned e^x into sin(x) or cos(x). Something about how those were really related just struck me as awesome.
So, how many of us uber-geeks started their study and fascination of fractals with the program Fractint?
I still have a copy on my PC!
Imaginary numbers are just junk science, like AGW at the liebrul NYT…