The HailStone sequence is a list of numbers which begins with a positive integer 'seed.' Even seeds are divided by two; odds, multiplied by 3 and increased by one. Subsequent values are treated similarly. Curiously, the sequence always ends by reaching '1'. (If you continue past that, you get a repeating pattern of 4-2-1-4-2-1 etc). This raises the question: Will all sequences of this nature always reach one? That problem is currently unsolved. Why is it called the HailStone sequence? Find out here.

We track the maximum height and the length of the sequence (iterations plus 1), its aspect ratio (the ratio of maximum height to initial seed) and its 'jitter': (the number of odd values less one). Unquestionably, there are other patterns to be explored in this mathematical oddity.

Learn more about the sequence here!

Note: For comparison purposes, check out a previous version of Hailstone from Past Blasts. This current version is an improvement in that it is responsive, but it also adds some extras like a graph grid with scales and the ability to copy the image and the data to the clipboard.

Last update: 11/22/19

---