Tag Archives: visualization

The chocolate bar game: variants

Posted on February 1, 2016 by Brent

Remember the chocolate bar game? Today I want to talk about some variants. Recall that the losing positions for the chocolate bar game can be visualized like this: What if we specify that you win if you end with a … Continue reading →

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The chocolate bar game: losing positions characterized

Posted on January 20, 2016 by Brent

The evident pattern from my last post is that losing positions in the chocolate bar game appear to be characterized by those where the binary expansion of is the same as the binary expansion of with any number (including zero) … Continue reading →

Posted in challenges, games, pattern, pictures | Tagged , , , , , , , , | 1 Comment

The chocolate bar game: losing positions in binary

Posted on January 18, 2016 by Brent

Recall the chocolate bar game from my last post, whose winning and losing positions can be visualized like this: Here’s a list of some losing positions on or above the main diagonal (dark blue squares in the above picture), ordered … Continue reading →

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The chocolate bar game

Posted on January 14, 2016 by Brent

Suppose there is an rectangle. I like to think of it as one of those bars of chocolate made up of squares: Two players take turns. On a player’s turn, she must break the chocolate bar along any one of … Continue reading →

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Animated Sieve of Eratosthenes

Posted on April 11, 2013 by Brent

Here’s something I made yesterday! (Note, I strongly suggest watching it fullscreen, in HD if you have the bandwidth for it.) Can you figure out what’s going on? The source code for the animation is here; I was inspired by … Continue reading →

Posted in arithmetic, counting, pattern, pictures, primes, video | Tagged , , , , | 12 Comments

Stars of the Mind’s Sky with Diagrams

Posted on April 6, 2013 by Brent

A few weeks ago, Paul Salomon posted a really beautiful work of mathematical art on his blog, Lost In Recursion: Stars of the Mind’s Sky, by Paul Salomon He included a precise mathematical description of the image, and I naturally … Continue reading →

Posted in geometry, group theory, pictures, programming | Tagged , , , , , | 9 Comments

Visualizing Pascal’s triangle remainders

Posted on October 20, 2012 by Brent

In a comment on my previous post, Juan Valera mentioned something about visualizing multiples of prime numbers in Pascal’s Triangle: In college, there was a poster with different Pascal Triangles, each of them highlighting the multiples of different prime numbers. … Continue reading →

Posted in fractals, modular arithmetic, pascal's triangle, pattern, pictures | Tagged , , | 15 Comments

Visualizing nim-like games

Posted on August 16, 2012 by Brent

Inspired by the comments on this post, I’ve had some ideas brewing for a while—I’m just only now getting around to writing them up. The topic is visualizing winning strategies for "nim-like" games. What do I mean by that? By … Continue reading →

Posted in games, pattern, pictures | Tagged , , , | 4 Comments