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    Original file (SVG file, nominally 1,280 × 660 pixels, file size: 1.05 MB)

    Summary

    Description
    English: Plot of Thomae's function on the interval (0,1). Shown are all rational points with denominator at most 200. The topmost point in the middle shows f(1/2) = 1/2

    Created using the following Java code:

    public class Thomae {
    	
    	static int gcd(int a, int b) {
    		while(a>0 && b>0) {
    			if(a>b) a -= a/b*b;
    			else b -= b/a*a;
    		}
    		return a>0 ? a : b;
    	}
    	
    	public static void main(String[] args) {
    		int max = 200;
    		
    		int width = 1280;
    		int height = 660;
    		
    		int border = 20;
    		int x0 = border;
    		int x1 = width - border;
    		double dx = x1-x0;
    		int y0 = height - border;
    		double dy = -dx;
    		int r=5;
    		
    		System.out.println("<?xml version=\"1.0\" standalone=\"no\"?>");
    		System.out.println("<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\" \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">");
    		System.out.println("<svg width=\""+ width +"\" height=\""+ height +"\" xmlns=\"http://www.w3.org/2000/svg\" version=\"1.1\">");
    		
    		for(int q=1; q<max; q++) for(int p=0; p<q; p++) if(gcd(p, q) == 1) {
    			System.out.println("  <circle cx=\""+ (x0+dx*p/q) + "\" cy=\""+ (y0+dy*1/q) +"\" r=\""+ r +"\" fill=\"black\" stroke=\"none\" />");
    		}
    		
    		System.out.println("</svg>");
    	}
    	
    }
    
    Date
    Source Own work
    Author Smithers888
    SVG development
    InfoField
     The SVG code is valid.
     This vector image was created with Java.

    Licensing

    Public domain I, the copyright holder of this work, release this work into the public domain. This applies worldwide.
    In some countries this may not be legally possible; if so:
    I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.

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    9 October 2008

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    Date/TimeThumbnailDimensionsUserComment
    current18:09, 9 October 2008Thumbnail for version as of 18:09, 9 October 20081,280 × 660 (1.05 MB)Smithers888{{Information |Description={{en|1=Plot of Thomae's function on the interval (0,1). Shown are all rational points with denominator at most 200. Created using the following Java code: <source lang="java"> public class Thoma

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