The Well-Tempered Palette (Part 2)

July 17, 2018

Last week, we’ve had a look at how to distribute maximally different colors on the RGB cube. But I also remarked that we could use some other color space, say HSV. How do we distribute colors uniformly in HSV space?

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Paeth’s Method (Square Roots, Part VII)

March 13, 2018

In Graphics Gems [1], Paeth proposes a fast (but quite approximate) method for the rapid computation of hypotenuse,

\displaystyle h=\sqrt{x^2+y^2}.

The goal here is to get rid of the big bad \sqrt{} because it is deemed “too expensive”—I wonder if that’s still actually true. First, he transforms the above equation:

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Random Points on a Sphere (Generating Random Sequences III, Revisited)

February 27, 2018

While searching for old notes—that I haven’t found anyway—I returned to an old blog entry and I thought I was kind of unsatisfactory, with be best part being swept under the carpet with a bit a faery dust, and very handwavingly.

So let’s work-out how to uniformly distribute points on a sphere in a more satisfactory fashion.

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Square roots (Part VI)

February 20, 2018

I’ve discussed algorithms for computing square roots a couple of times already, and then some. While sorting notes, I’ve came across something interesting: Archytas’ method for computing square roots.

Archytas’ method is basically the old Babylonian method, where you first set

a=1,

b=n,

and iterate

\displaystyle a'=\frac{a+b}{2},

\displaystyle b'=\frac{n}{a'}=\frac{2n}{a+b},

until desired precision is achieved (or the scribe is exhausted).

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Unary numbers.

February 13, 2018

A positional number system needs a base that is either greater than one, or smaller than minus one—yes, we can have a negative base for a number system. The system, however, seems to break down if the base we chose is base 1.

If the base is 1, then there are no permissible digits since the digits d, in a base b system, must be 0\leqslant{d}<b. But we can still represent numbers using just 1s. That's the unary numeral system, and numbers are just represented as repeated 1s. 15? Fifteen ones: 111111111111111. Operations? Not very complicated, just… laborious.

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Elementary Automata (Generating Random Sequences XI)

February 6, 2018

So 3-cells context elementary automata seem too “self-correcting” to be useful pseudo-random generators. What if we fixed that boundary problem and have the automaton run on a cylinder (with both end joined)? What if we augment the context from 3 to 5 cells?

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Elementary Automata (Generating Random Sequences X)

January 30, 2018

I was rather discontented with last week’s post results. Most automata seemed to produce self-correcting patterns, even when seeded randomly—one could argue that rand() isn’t the strongest random generator, but that wasn’t the problem. No, indeed, most automata exhibit self-correcting behavior, forming the same self-similar pattern, or worse, the same periodic pattern.

So I made a few more experiments with random seeds and larger images. The code isn’t very complicated and isn’t of interest in itself, but it reveals a couple of interesting things.

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