# Game of Life, Part 1, The Rule 1

Posted by **Cleve Moler**,

**Category:**- Matrices

Blogs

Posted by **Cleve Moler**,

This is part one of a series of posts about John Conway's Game of Life. One deceptively simple rule leads to an incredible variety of patterns, puzzles, and unsolved mathematical problems, and a beautiful use of MATLAB sparse matrices.
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**Category:**- Matrices

Posted by **Cleve Moler**,

The first MATLAB trade show booth at the CDC in December, 1984, included a potted palm.... read more >>

**Category:**- History

Posted by **Cleve Moler**,

This is the third part of a series of posts about Marc Kac's 1966 paper in the American Mathematical Monthly [1]. This part is devoted to the proof that the drums have the same eigenvalues.
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**Category:**- Eigenvalues

Posted by **Cleve Moler**,

This is the second part of a series of posts about Marc Kac's 1966 paper in the American Mathematical Monthly [1]. This part is devoted to contour plots of the eigenfunctions.
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**Category:**- Eigenvalues,
- Graphics

Posted by **Cleve Moler**,

The title of this multi-part posting is also the title of a 1966 article by Marc Kac in the American Mathematical Monthly [1]. This first part is about isospectrality.
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**Category:**- Eigenvalues

Posted by **Cleve Moler**,

How do you compute the hypotenuse of a right triangle without squaring the lengths of the sides and without taking any square roots?... read more >>

**Category:**- Algorithms

Posted by **Cleve Moler**,

I have been interested in the computation of the matrix exponential, $e^A$, for a long time. A recent query from a user provides a provocative example.... read more >>

**Category:**- Matrices

Posted by **Cleve Moler**,

MATLAB has two different functions for piecewise cubic interpolation, `spline` and `pchip`. Why are there two? How do they compare?
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**Category:**- Algorithms

Posted by **Cleve Moler**,

We all know that Friday the 13th is unlucky, but is it unlikely?... read more >>

**Category:**- Fun

Posted by **Cleve Moler**,

An esoteric fact about matrices is that any real matrix can be written as the product of two symmetric matrices. I've known about this fact for years, but never seriously explored the computational aspects. So I'm using this post to clarify my own understanding of what I'll call the *symmetric pair decomposition*. It turns out that there are open questions. I don't think we know how to reliably compute the factors. But I also have to admit that, even if we could compute them, I don't know of any practical use.... read more >>

**Category:**- Matrices

*These postings are the author's and don't necessarily represent the opinions of MathWorks.*

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