Blog Archives

Those dice aren’t loaded, they’re just strange

June 18, 2010
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Those dice aren’t loaded, they’re just strange

I must confess to feeling an almost obsessive fascination with intransitive games, dice, and other artifacts. The most famous intransitive game is rock, scissors, paper. Rock beats scissors.  Scissors beats paper. Paper beats rock. Everyone older than 7 seems to know this, but very few people are aware that dice can exhibit this same behavior,

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Repulsive dots pattern, the difference of distance

June 14, 2010
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Repulsive dots pattern, the difference of distance

What if you wanted to randomly place objects into a field, and the more objects you had, the more they rejected newcomers placed nearby? To find out, I setup a simulation. The code, shown at the end, isn’t all that interesting, and the plots shown below aren’t all that special. I think there is one

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A different way to view probability densities

June 12, 2010
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A different way to view probability densities

The standard, textbook way to represent a density function looks like this: Perhaps you have seen this before? (Plot created in R, all source code from this post is included at the end). Not only will you find this plot in statistics books, you’ll also see it in medical texts, sociology, and even economics books.

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Betting on Pi

May 31, 2010
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Betting on Pi

I was reading over at math-blog.com about a concept called numeri ritardatari. This sounds a lot like “retarded numbers” in Italian, but apparently “retarded” here is used in the sense of “late” or “behind” and not in the short bus sense. I barely scanned the page, but I think I got the gist of it:

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Weekend art in R (part 1?)

May 29, 2010
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Weekend art in R (part 1?)

As usual click on the image for a full-size version. Code: par(bg="black") par(mar=c(0,0,0,0)) plot(c(0,1),c(0,1),col="white",pch=".",xlim=c(0,1),ylim=c(0,1)) iters = 500 for(i in 1:iters) { center = runif(2) size = rbeta(2,1,50)   # Let's create random HTML-style colors color = sample(c(0:9,"A","B","C","D","E","F"),12,replace=T) fill = paste("#", paste(color[1:6],collapse=""),sep="") brdr = paste("#", paste(color[7:12],collapse=""),sep="")   rect(center[1]-size[1], center[2]-size[2], center[1]+size[1], center[2]+size[2], col=fill, border=brdr, density=NA, lwd=1.5) }

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R: More plotting fun with Poission

May 28, 2010
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R: More plotting fun with Poission

Coded as follows: x = seq(.001,50,.001) par(bg="black") par(mar=c(0,0,0,0)) plot(x,sin(1/x)*rpois(length(x),x),pch=20,col="blue")

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The guessing game in R (with a twist, of course)

May 27, 2010
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Maybe you remember playing this one as a kid. If you are about my age, you may have even created a version of this game as one of your first computer programs. You guess a number, the computer tells you if you if you are too low or high. I’ve limited the number of maximum

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Zone of instability

May 26, 2010
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Zone of instability

I woke up from my afternoon nap feeling a bit off-kilter, so I decided to go for another random walk. In particular, I wanted a journey that avoided the center, but didn’t just run for an exit either. After playing around for a while I came up with this: # Take a wacky walk, return

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How many tanks? MC testing the GTP

May 25, 2010
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How many tanks? MC testing the GTP

It’s 1943 and you work for the good guys. A handful of German tanks have been captured, and each one has a serial number. This is back when serial numbers were still presumed to come in serial, one right after the other. Given your collection of numbered tanks, and assuming that any existing tank was

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