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Welcome to Fractal Forums > Fractal Math, Chaos Theory & Research > General Discussion > Quater-imaginary base
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Author Topic: Quater-imaginary base  (Read 1685 times)
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jwm-art
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« 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

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  grin
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kram1032
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« Reply #1 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 smiley
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jwm-art
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« Reply #2 on: January 26, 2010, 03:56:56 PM »
Quote from: kram1032 on January 26, 2010, 03:40:13 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.
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kram1032
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« Reply #3 on: January 26, 2010, 04:15:22 PM »
ah, I see...

well, that could change things a bit, maybe smiley
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