Title: Quater-imaginary base Post by: jwm-art on January 26, 2010, 04:57:51 AM Quater-imaginary base is a non-standard positional numeral system proposed by Don Knuth (programmers may have heard of him).
http://en.wikipedia.org/wiki/Quater-imaginary_base (http://en.wikipedia.org/wiki/Quater-imaginary_base) It's all a bit beyond my ken, but was curious as to if any novel uses could be made of it in the world of fractal plotting. For instance I wondered if the M-set could use the normal decimal based complex numbers to feed into an equation which performed the calculations in the quater imaginary base. Or would that be a bit too much of a quatermess ;D Title: Re: Quater-imaginary base Post by: kram1032 on January 26, 2010, 03:40:13 PM ah, that one....
Well, this should actually just return the Mandelbrot as always. The difference is, that it uses, well, a different base. However, the computer doesn't calculate in a base-10-system but rather converts the output to that just so we can better read what's meant.# The theoretical (however, afaik not practical, because processors don't make use of this) advantage would be, that complex valued functions could be caluculated faster, as far as I know... However, you can visualize nice fractal-like structures with that anyway :) Title: Re: Quater-imaginary base Post by: jwm-art on January 26, 2010, 03:56:56 PM ah, that one.... Well, this should actually just return the Mandelbrot as always. I meant, to use the normal decimal based complex numbers fed into the quater imaginary base equation - without actually doing any conversion from one to the other. More of a literal translation, not actually performing a real conversion between the two bases, simplified example: decimal float -0.212392929 >> string "-0.212392929" >> quater-imaginary-base -0.2123929 Just a curiosity. Title: Re: Quater-imaginary base Post by: kram1032 on January 26, 2010, 04:15:22 PM ah, I see... well, that could change things a bit, maybe :) |