It would be fitting to use Circos to visualize the digits of pi, since what is more round than Circos? Circos is a software package for visualizing data and information. It visualizes data in a circular layout — this makes Circos ideal for exploring relationships between objects or positions.

*Click "Read More" to continue!*### Circos Art Of π — Digit Transition Paths

The position of the link on a digit's segment is associated with the position of the digit π. For example, the "14" link associated with the 2nd digit (1) and the 3rd digit (4) is drawn from position 2 on the 1 segment to position 3 on the 4 segment.

As more digits are added to the path, the image becomes a weaving mandala.

### Circos Art Of π, φ And e — Transition Paths And Bubbles

For a given digit, the chance that the next 5 digits are the same is 0.00001 (0.1 that the next digit is the same * 0.1 that the second-nex digit is the same * ...). Therefore the chance that a given position the next 5 digits are not the same is 1 - 1/0.00001 = 0.99999. From this, the chance that k consecutive digits don't initiate a 6-digit sequence is therefore 0.99999k.

If I ask what is k for which this value is 0.5, I need to solve 0.99999k, which gives k = 69,314. Thus, chances are 50-50 that in a 69,000 digit random sequence we'll see a run of 6 idendical digits. This calculation is an approximation.

It's fun to look for words in π. For example, love appears at 13,099,586th digit.

### A Tangent to Randomness

### Circos Art Of π — Heaps Of Bubbles

*ij*, a dot is placed on

*i*th's segment at the position of

*i*colored by

*j*.

segment | position | colored_by |
---|---|---|

3 | 0 | 1 |

1 | 1 | 4 |

4 | 2 | 1 |

1 | 3 | 5 |

5 | 4 | 9 |

9 | 5 | 2 |

2 | 6 | 6 |

### Spiral Art of π

*r*=

*a*+

*b*θ and has the interesting property that a ray from the origin will intersect the spiral every 2π

*b*. Thus, each spiral can accomodate inscribed circles of radius π

*b*.

Why the Brewer palette? These color schemes have some very useful perceptual properties and are commonly used to encode quantitative and categorical data.