Spatial and Audio Visualizations of Prime Number Distributions

I have been thinking a lot recently about the distribution of prime numbers — in particular, I’ve been trying to figure out if there is a way to predict the sequence of gap sizes between primes. But anyway, in the course of that investigation I came across a really cool site about number spirals in which the author develops a set of formulas and insights from them based on a particular way of aligning numbers in spirals. It’s a very interesting, visual, site that anyone who knows basic algebra can understand. I wonder if some of the properties of these spirals relate to physics — particularly the orbits of planets or the positions of particles?

I also found this site which has several illustrations on it of various spatial visualizations of primes — the one I found most interesting is the “Golbach Folding at Multiples of 30,” a way to make the primes line up (with one minor catch!).

This is another interesting site that provides music generated by prime number sequences that sounds suspiciously like free-jazz.

As long as we’re on the subject — I just found this obscure research paper that shows the prime numbers at work in nature — they find that predator-prey interactions obey patterns that tend to favor prime numbers. Interesting. This adds to my hunch that the primes play an important role in nature — and that they may be fundamental to understanding the patterns at work in chaotic dynamical systems.

One thought on “Spatial and Audio Visualizations of Prime Number Distributions

  1. see UA Mathematicians Predict Patterns in Fingerprints, Cacti
    “When a line is drawn from sticker to sticker on a cactus in a clockwise or in a counterclockwise direction, the line ends up spiraling around the plant. This occurs in many plants, including pineapples and cauliflower. When these spirals are counted, it results in numbers that belong to the Fibonacci sequence, a series of numbers that appears frequently when scientists and mathematicians analyze natural patterns.
    From his model, Shipman found that the initial curvature of a plant near its growth tip influences whether it will form ridges or hexagons. He found that plants with a flat top, or less curved top, such as saguaro cacti, will always form ridges and tend not to have Fibonacci sequences. Plants that have a high degree of curvature will produce hexagonal configurations, such as those in pinecones, and the number of spirals will always be numbers in the Fibonacci sequence.
    Newell says that Shipman’s mathematical model demonstrates that the shapes chosen by nature are those that take the least energy to make. “Of all possible shapes you can have, what nature picked minimizes the energy in the plant.” “

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