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Tag: Math

OVM Pseudo-Algebra and Surreal Numbers

By Zevan

Was just watching this funny video on Numberphile:

Here is the Surreal Numbers book on archive.org:

https://archive.org/stream/SurrealNumbers/Knuth-SurrealNumbers#page/n7

Got a kick out of the story around this stuff… When Knuth shows the notation for surreal numbers I suddenly remembered a weird program I’d written awhile back.

OVM

I had been out drawing in my sketchbook one sunday (almost 2 years ago) and found myself creating a tiny little system of symbols:

A few days later I speed coded a version of the system. Apparently I had posted a screenshot on FB while I was working on it:

See if you can figure out how it works. I’m sure the code could be cleaned up a bit…

While OVM has little/nothing to do with Surreal Numbers – I’m glad the video reminded me it…

Read snippet: OVM Pseudo-Algebra and Surreal Numbers

Hermit Crab Curve as PRNG (a deterministic pseudo-random number generator with contrast and smoothness – inspired by stochastic and organic randomness)

By Zevan

Around 2015 I had the idea for a PRNG that would clamp itself and have moments of “smoothness”. When I got around to trying to create such a thing, the result was something I jokingly called the “Hermit Crab Curve”. I also called it the “Shard Curve”.

The equation for the curve defines a radius in polar coordinates:

Where a and d are paramters that control the detail of the curve. o is a rotation and offset value for the angle and s is a scalar. Note the use of rem. The resulting curve is much less interesting if a standard modulo is used in place of a remainder:

The above variable values were found using this interactive version of the equation:

To illustrate how you might use this as a PRNG I created this fork of the above pen:

That, in combination with the information from my other article from yesterday… Should be enough to see what I mean.


You can read the original description of the Hermit Crab Curve that I created using ArcType here:

http://zevanrosser.com/arctype-dev/hermit-crab-curve.html

If you end up using this for something interesting let me know. I’d love to see it 😀

Read snippet: Hermit Crab Curve as PRNG (a deterministic pseudo-random number generator with contrast and smoothness – inspired by stochastic and organic randomness)

Harmonic Series

By Zevan
var harmonic:Number = 0;
var k:Number = 1;
addEventListener(Event.ENTER_FRAME, onLoop);
function onLoop(evt:Event):void {
	 harmonic += 1 / k;
	 trace("+");
	 trace("1 / " + k + "              =              " + harmonic);
	 k+=1;
}

Read more about the harmonic series at wikipedia.


1 / 1 = 1
+
1 / 2 = 1.5
+
1 / 3 = 1.8333333333333333
+
1 / 4 = 2.083333333333333
+
…

Read snippet: Harmonic Series