[Solved] Mandelbrot Set pixelation, failed to solve with BigDecimal.

[Jameth13]

Hi,

I am trying to render the Mandelbrot Set. I have implemented it successfully with this code using doubles:

public class MandelbrotSetDouble {
	
	
	private int width;
	private int height;
	
	private double x, y, xc, yc, tmp;
	
	
	public MandelbrotSetDouble(int width, int height) {
		
		
		this.width = width;
		this.height = height;
		
		
	}
	
	
	
	public ArrayList<Tuple3Int> loop(double zoom, double offSetX, double offSetY, int maxIter) {
		

		ArrayList<Tuple3Int> list = new ArrayList<Tuple3Int>();
		

		
		for (int ix = 0; ix < width; ix++) {
			
			for (int iy = 0; iy < height; iy++) {
				
				
				x = y = 0;
				xc = ((ix - (width / 2)) / zoom) + offSetX;
				yc = ((iy - (height / 2)) / zoom) + offSetY;
				
				
				for (int iter = 0; iter < maxIter; iter++) {
					
					
					if (((x * x) + (y * y)) < 4) {
						
						tmp = x * x - y * y + xc;
						y = 2.0 * x * y + yc;
						x = tmp;
						
					}else{
						
						list.add(new Tuple3Int(ix, iy, iter));
						break;
						
					}
					
					
				}
				
				
			}
			
		
		}
		
		
		return list;	
		
		
	}
	
	
	
}

Then I converted all the code to using BigDecimal so I could render deeper into the Mandelbrot Set:

public class MandelbrotSetBD {
	
	
	private int width;
	private int height;
	
	private int scale = 32;
	private int round = 0;
	
	private BigDecimal x = new BigDecimal("0").setScale(scale, round);
	private BigDecimal y = new BigDecimal("0").setScale(scale, round);
	private BigDecimal xc = new BigDecimal("0").setScale(scale, round);
	private BigDecimal yc = new BigDecimal("0").setScale(scale, round);
	private BigDecimal temp1 = new BigDecimal("0").setScale(scale, round);
	private BigDecimal temp2 = new BigDecimal("0").setScale(scale, round);
	private BigDecimal four = new BigDecimal("4").setScale(scale, round);
	private BigDecimal two = new BigDecimal("2").setScale(scale, round);
	
	
	public MandelbrotSetBD(int width, int height) {
		
		
		this.width = width;
		this.height = height;
		
		
	}
	
	
	
	public ArrayList<Tuple3Int> loop(String zoom, String offSetX, String offSetY, int maxIter) {
		
		
		System.out.println("Starting generating Mandelbrot Set using BigDecimal with scale=" + scale + "...");
		
		ArrayList<Tuple3Int> list = new ArrayList<Tuple3Int>();
		BigDecimal offSetXbd = new BigDecimal(offSetX);
		BigDecimal offSetYbd = new BigDecimal(offSetY);
		BigDecimal zoombd = new BigDecimal(zoom);
		BigDecimal ixbd;
		BigDecimal iybd;
		BigDecimal widthbd;
		BigDecimal heightbd;
		
		
		for (int ix = 0; ix < width; ix++) {
			
			for (int iy = 0; iy < height; iy++) {

				ixbd = new BigDecimal(String.valueOf(ix));
				iybd = new BigDecimal(String.valueOf(iy));
				widthbd = new BigDecimal(String.valueOf(width));
				heightbd = new BigDecimal(String.valueOf(height));
				
				x = new BigDecimal("0").setScale(scale, round);
				y = new BigDecimal("0").setScale(scale, round);
				xc = ixbd.subtract(widthbd.divide(two));
				xc = xc.multiply(zoombd);
				xc = xc.add(offSetXbd);
				yc = iybd.subtract(heightbd.divide(two));
				yc = yc.multiply(zoombd);
				yc = yc.add(offSetYbd);
				
				
				for (int iter = 0; iter < maxIter; iter++) {

					temp1 = x.multiply(x).setScale(scale, round);
					temp1 = temp1.add(y.multiply(y)).setScale(scale, round);
					
					if (temp1.compareTo(four) == -1) {
						
						temp2 = x.multiply(x).setScale(scale, round).subtract(y.multiply(y).setScale(scale, round)).setScale(scale, round).add(xc).setScale(scale, round);
						y = two.multiply(x).setScale(scale, round).multiply(y).setScale(scale, round).add(yc).setScale(scale, round);
						x = temp2.setScale(scale, round);
						
					}else{
						
						list.add(new Tuple3Int(ix, iy, iter));
						break;
						
					}
					
					
				}
				
				
			}
			
		
		}
		
		
		System.out.println("Done!");
		return list;	
		
		
	}
	
	
	
}

With the scale set to 32 it should be twice as accurate as a double but it pixelates at the EXACT same point. Even when I change the scale to anywhere from 16 to 64 it makes NO DIFFERENCE.
I am completely stumped.
I can't run the code without scaling the BigDecimals because it takes far too long to compute the set.

I think I must have a bottleneck somewhere that is stopping me from seeing the benefits from using BigDeciomal but I can't find it.


Thank you in advance for any of your suggestions,
James


For those who are interested, you can download the latest version of my Mandelbrot Set generator here:
https://mega.co.nz/#!iIVimQaY!KPIMO84fkjWUm8ZLvbNp8lsBd5Mi1B6abo4GKEofooc.
Please let me know what you think so far!
(This version is using doubles.)

[Jameth13]

I honestly have no idea how, but I've fixed it!
I was messing around, trying to debug it when it just worked all of a sudden.
I can now render the Mandelbrot Set as deep as I am willing to wait for.

Here is the latest version, if you're interested:
https://mega.co.nz/#!GUNw1RTR!Fa2m2nIFJcBpsW_oUWGRTgtYJD-h1zbYRUOjJGngqew

I will leave the thread open, feedback welcome!

James