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Active Forums => Programs => Topic started by: Ashish on October 19, 2019, 02:18:43 am

Title: Prime Numbers Fractal
Post by: Ashish on October 19, 2019, 02:18:43 am
Hi everyone! :D
I have recently watched 3Blue1Brown's video on prime number where he plots (p,p) in polar Cartesian plane where p is a prime number.
I did the same thing but with a twist and it seems like I have created a new fractal.
Run the program & Enjoy!
Code: QB64: [Select]
  1. 'Prime Number Fractal By Ashish
  2. '19 Oct, 2019
  3. _TITLE "Prime Number Fractal By Ashish"
  4. SCREEN _NEWIMAGE(700, 700, 32)
  5. s = 1
  7.     s = s + 25
  8.     FOR i = 1 TO s
  9.         IF isPrime(i) THEN
  10.             xx = map(COS(i) * i, 0, s, 0, s / 16) * COS(z) + _WIDTH / 2
  11.             yy = map(SIN(i) * i, 0, s, 0, s / 16) * SIN(z) + _HEIGHT / 2
  12.             r = map(ABS(xx - 350), 0, 350, 255, 50)
  13.             g = map(ABS(yy - 350), 0, 350, 255, 50)
  14.             PSET (xx, yy), _RGB32(r, g, (r + g) / 2, 100)
  15.         END IF
  16.     NEXT
  17.     _DISPLAY
  18.     _LIMIT 48
  19.     z = z + .1
  20. LOOP UNTIL s > 10000
  21. FUNCTION isPrime (n AS INTEGER)
  22.     k = 0
  23.     IF n < 2 THEN EXIT FUNCTION
  24.     FOR i = 2 TO n
  25.         IF n MOD i = 0 THEN k = k + 1
  26.         IF k > 1 THEN EXIT FUNCTION
  27.     NEXT
  28.     IF k = 1 THEN isPrime = -1
  30. 'from p5js.bas
  31. 'https://bit.ly/p5jsbas
  32. FUNCTION map! (value!, minRange!, maxRange!, newMinRange!, newMaxRange!)
  33.     map! = ((value! - minRange!) / (maxRange! - minRange!)) * (newMaxRange! - newMinRange!) + newMinRange!
  35.  

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Title: Re: Prime Numbers Fractal
Post by: Petr on October 19, 2019, 05:20:25 am
Hi Ashish,

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Title: Re: Prime Numbers Fractal
Post by: bplus on October 19, 2019, 10:29:07 am
Hi Ashish,

This is nice graphic even without Prime Numbers!

Code: QB64: [Select]
  1. 'Prime Number Fractal By Ashish
  2. '19 Oct, 2019
  3. _TITLE "Prime Number Fractal By Ashish mod B+ without Prime Numbers"
  4. SCREEN _NEWIMAGE(700, 700, 32)
  5. s = 1
  7.     s = s + 10
  8.     FOR i = 1 TO s
  9.         IF RND > .8 THEN
  10.             xx = map(COS(i) * i, 0, s, 0, s / 16) * COS(z) + _WIDTH / 2
  11.             yy = map(SIN(i) * i, 0, s, 0, s / 16) * SIN(z) + _HEIGHT / 2
  12.             r = map(ABS(xx - 350), 0, 350, 255, 50)
  13.             g = map(ABS(yy - 350), 0, 350, 255, 50)
  14.             PSET (xx, yy), _RGB32(r, (r + g) / 2, g, 10)
  15.         END IF
  16.     NEXT
  17.     _DISPLAY
  18.     _LIMIT 48
  19.     z = z + .1
  20. LOOP UNTIL s > 10000
  21. FUNCTION map! (value!, minRange!, maxRange!, newMinRange!, newMaxRange!)
  22.     map! = ((value! - minRange!) / (maxRange! - minRange!)) * (newMaxRange! - newMinRange!) + newMinRange!
  24.  
Title: Re: Prime Numbers Fractal
Post by: Ashish on October 19, 2019, 10:46:07 am
@Petr
Thanks!
@Bplus
Cool. It resembles like the original one. I choose prime number because they less in number.
Title: Re: Prime Numbers Fractal
Post by: bplus on October 19, 2019, 11:35:52 am
Quote
because they less in number.

Ah density, modulus would have much more control of density PLUS uniforimty!

Here is increasing Modulus = m (decreasing density) gives us a little intuitive look at the drawing algorithm.
Code: QB64: [Select]
  1. 'Prime Number Fractal By Ashish
  2. '19 Oct, 2019
  3. _TITLE "Prime Number Fractal By Ashish mod B+ without Prime Numbers"
  4. SCREEN _NEWIMAGE(700, 700, 32)
  5. s = 1
  6. m = 5
  8.     m = m + 5
  9.     s = 0
  10.     CLS
  11.     DO
  12.         s = s + m
  13.         FOR i = 1 TO s
  14.             IF i MOD m = 0 THEN
  15.                 xx = map(COS(i) * i, 0, s, 0, s / 16) * COS(z) + _WIDTH / 2
  16.                 yy = map(SIN(i) * i, 0, s, 0, s / 16) * SIN(z) + _HEIGHT / 2
  17.                 r = map(ABS(xx - 350), 0, 350, 255, 50)
  18.                 g = map(ABS(yy - 350), 0, 350, 255, 50)
  19.                 PSET (xx, yy), _RGB32(r, (r + g) / 2, g, 100)
  20.             END IF
  21.         NEXT
  22.         _DISPLAY
  23.         _LIMIT 100
  24.         z = z + _PI(1 / 36)
  25.     LOOP UNTIL s > 10000
  26.     _DELAY 1
  28. FUNCTION map! (value!, minRange!, maxRange!, newMinRange!, newMaxRange!)
  29.     map! = ((value! - minRange!) / (maxRange! - minRange!)) * (newMaxRange! - newMinRange!) + newMinRange!
  31.  
  32.  
  33.  

Title: Re: Prime Numbers Fractal
Post by: Ashish on October 20, 2019, 03:59:29 am
@Bplus
Wow! So, a lot of more pattern can be generated with this. Cool!
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