Prime Spiral on Honeycomb Grid

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According to wikipedia and another document, drawing prime number on grid in spiral order,then many of line will appear by 45 slant. I thought what will happen if I draw them on honeycomb (hex) grid? I tried to search for internet but not found. That's why I tried to draw it.

What do I try to draw?

In uram's spiral, numbers are on square grid and filled if it is prime. Here I try to set numbers on honeycomb grid and fill some color on prime grid. Sorry for dirty image .

image

The red point at the center is the starting point.This is 0. The right-up is 2. left to 2 is 3. left-bottom of 0 is 5. I draw it until 10000. Clicking this image , you will see large image. (2000*2000. up to 100000)
I thought this image will divided to 6 area. but the line appear in three area, bottom and bottom-right area and up and up-right and left-up and left-bottom. There might be some rule, isn't it?

Draw on browser

I thought it is interesting if you can see drawing image.Here Javascript draw it. Please browse this page by newer modern browser because of HTML5 and canvas.

Animation in reverse order

Prime numbers are drawn from the center starting with 2 in previous image. Here I created the animation the prime sequence grows as spiral from the center. It sounds like to have long time by JavaScript, I create movie . How about this rounding like movie?

It is very interesting to appear slant line in bottom and right-bottom area. (I believe this calculation is correct...)

Another more good idea?

There is many kind of primes.I might be good if change the color as its type. (Mersenne prime, Euler prime number, Fermat prime number )
Centered one grid, I draw number sequence as rounding. But It may be interesting to draw sequence after thee grid arranged and surrounding the three grids. See image.

And more, start after four grids and surrounding , or start with more complex structure might became interesting image.
It may be interesting to draw on triangle grid.

I guess this research is good for the subject of the summer vacation of high school student. (but it may be needed to find some good or useful truth... not just for fun?) It is very hard for me to continue this!!

Source code to generate image for programmer

You can check and see JavaScript code from this html source code of this page. And Java program to draw this is available. NO WARRANTIES.

This document is licenced by Attribution 2.1 Japan (CC BY 2.1) creative commons BY

Published : 2011-12-04
Last updated : $Date: 2013-03-01 23:48:55 +0900 (Fri, 01 Mar 2013) $

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