Yes? No? Maybe? (Part I)

Initializing arrays, or any variable for that matter, is always kind of a problem. Most of the times, you can get away with a default value, typically zero in C#C++, but not always. For floats, for example, NaN makes much more sense. Indeed, it’s initialized to not a number: it clearly states that it is initialized, consciously, to not a value. That’s neat. What about integers? Clearly, there’s no way to encode a NaI (not an integer), maybe std::numeric_limits::min(), which is still better than zero. What about bools?

Bool is trickier. In C++, bool is either false or true, and weak typing makes everything not zero true. However, if you assign 3 to a bool, it will be “normalized” to true, that is, exactly 1. Therefore, and not that surprisingly, you can’t have true, false, and maybe. Well, let’s fix that.

Paeth’s Method (Square Roots, Part VII)

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

.

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

Encoding seeds

I was discussing procedural generation with one of my students when he brought up The Binding of Isaac, that delightfully quirky and creepy rogue-like game. One of the interesting features of the game is that the dungeons are randomly generated and that you can get the seeds for the dungeons and share them. A typical seed looks something like this:

QNFQ 8H7Z

So what does it encode?

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

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.

Square roots (Part VI)

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

,

,

and iterate

,

,

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

Unary numbers.

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 , in a base system, must be . 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.

Elementary Automata (Generating Random Sequences XI)

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?

Elementary Automata (Generating Random Sequences X)

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.

Elementary Automata (Generating Random Sequences IX)

A while ago, Wolfram (re)introduced elementary cellular automata, a special case of cellular automata that lives in one dimension. One cutesy aspect of these automata is that the rules are easy to describe and number. As any automata, it is given a context, a region of interest, and gives an output depending on the context. For example, we can have the rules:

Context	output
000	1
001	0
010	1
011	0
100	1
101	0
110	1
111	1

The output column can be viewed as a number, in this case 11010101, 0xd5, or 213. This is rule 213.

It may be tempting to use those to generate chaos, noise, and random numbers. But is it that a good idea?

Woe is coding.