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Sacks Spiral(Prime Spotter)

Image:
screenshot of the scene

Author: FRA32

Group: Technical

Filesize: 335.2 kB

Date added: 2016-01-10

Rating: 6.3

Downloads: 1742

Views: 509

Comments: 10

Ratings: 4

Times favored: 0

Made with: Algodoo v2.1.0

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An alternate version of my first Prime spotter, this scene spots primes and aligns them in the shape of an archimedic spiral(spiral which has it's radius increased by a linear value every rotation). The special property of this spiral is that it may be archimedic(or linear), but the numbers on it are squared, so every turn it reaches another square number(i.e. 1 turn = 1, 2 turns = 4, 3 turns = 9 and so on, BUT 1 turn = radius 1, 2 turns = radius 2, 3 turns = radius 3). Spotting primes on this spiral also yields a pattern that is less random than primes may appear on first glance, but still are not regular enough to be formulated in an uniform algorythm. There are algorythms that can spot a series of primes, but these only apply to a limited number range or are not garuanteed to yield primes, for example x^2 + 3x + 1 alias (x+1.5)^2-1.25

Legend:
The tracer marks the current location of the spotter as it progresses through the numbers. It will move at a constant speed, and calculate the next prime number while it moves. Should a prime number still be calculated while the spotter has already reached it, it pauses for a short while until it is done with calculating.
Green circles resemble non-prime square numbers. They are the ones the Spiral is mapped after, and are in the center of a wide prime-less area.
Red circles are the primes spotted by the algorythm.

Clicking on any circle results in it's number value to be displayed on a small box that's near the bottom right of your screen(depends on monitor size)

To increase the speed, 24 spotters are used simultaneously, each scanning a certain number range before vanishing.

UPDATE: Fixed a major calculation error that caused the code to output more primes than there actually exist.
Last edited at 2016/07/03 21:50:30 by FRA32
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Nicely done. I was wondering about what prime numbers would look like on a spiral, but I wasn't sure what kind of spiral to try. Now I get to see what it looks like without having to do any work.
Last edited at 2016/01/10 18:08:13 by s_noonan
Whoops, totally forgot to set timetolive to 0.05. Fixed it now.

What's really odd about these prime patterns is that, despite the fact that this archimedic/quadratic spiral is quite different from the square spiral of my other scene, the primes still form visible patterns that can even be expressed using formulas, even if these formulas frequently output a non-prime number. In an Java program of mine I made the program calculate the square spiral with all primes on it, but between each prime, it outputs the difference between the last 2 primes(i.e 3-2 = 1,5-3 = 2, 7-5 = 2 etc.). The beginning of this number chain looks like this:
1; 1; 2; 2; 4; 2; 4; 2; 4; 6; 2; 6; 4; 2; 4; 6; 6; 2; 6; 4; 2; 6; 4; 6; 8; 4; 2; 4; 2; 4; 14; 4; 6; 2; 10; 2; 6; 6; 4; 6; 6; 2; 10; 2; 4; 2; 12; 12; 4; 2; 4; 6; 2; 10; 6; 6; 6; 2; 6; 4; 2; 10; 14; 4; 2; 4; 14; 6; 10; 2...

I am pretty sure there is some complex pattern inside this, besides the fact that all numbers have to be even, except the first 2. Someone who is really in love with maths needs to analyze these patterns, the images resulting from the prime plotting algorythms, and many more things.
Maybe someday we own an algorythm that spits out primes at garuantee. What that would be usefull tho is questionable:lol:
Last edited at 2016/01/10 14:12:11 by FRA32
When you figure out the prime series, they will name it after you. You probably have as good of a chance of figuring it out as anybody else. Regarding the series of differences, that's an interesting approach. I did a similar thing where I was looking at the ratio of number of prime numbers to the total number of numbers as the square spiral progressed.
@FRA32 -- Holy cow! I am very impressed by your math and your programming abilities. If you were an "older" man, like kilinich and I are, I would certainly be impressed, but because you are so young (still in high school) I am doubly impressed. I can only imagine what you might do say, a decade from now! :o
Pretty trippy but there are some even numbers, not hating though. I like the advanced thyme. 8
Ohh dear, thank you for notifying me about this. I checked the code and noticed that the calculator did not reset the division counter when finding a non-prime-number, which caused it to skip numbers like /2, /3 etc. That's why there were even numbers and many more dots than actual primes. I fixed it now;)
Looks a bit like Fibonacci's spiral in the beginning
Yup, but thats also only because the primes are taking shape of polynomical spirals before lining of into a horizontal line. In the end this is a archimedic/linear spiral, and strangely enough we see nearly persistent lines of primes that can even be expressed as formulas with a success-chance of 80%(decreasing with highter values of X, as well as requiring X to be a natural number)
FRA: You... HOW
Whut di ya mean MoBuilds? How I make this kind of stuff?


MMMMMMMMMMMMagicc....al Thyme code