← Back to Generator

Configuration Parameters

Parameter Description Range
width Number of output image pixel width. Limited to at least 50 and at most 2000.
height Number of output image pixel height. Limited to at least 50 and at most 2000.
mod In modes product and sum fixed modulus for new composite number.

In mode jacobi the parameter mod is the fixed number n in jacobi-symbol an		 Limited to at least 1 and at most 10000 for all three modes.
norm Mapping of input pixel (x,y) → norm(x,y) Does not create a fractal image for (x,y) → x ⋅ y in modes product and sum.

Java-Code for mode product

public Color[][] product(final BiFunction<Long, Long, Long> fun, final long mod) {
	final long[][] colors = new long[pixelWidth][pixelHeight];
				
	java.util.stream.IntStream.range(1, pixelWidth + 1).parallel().forEach(i -> {
		for(int j = 1; j <= pixelHeight; j++) {
			final List<Long> primeFactors = new ArrayList<>();
			final List<Integer> expFactors = new ArrayList<>(), preSortExpFactors = new ArrayList<>();
			final Set<Long> visited = new HashSet<>();
			final long normBuf = fun.apply((long)i, (long)j);
			Map<Long, Integer> factors;
			long oldNorm = normBuf, happy = 0;
		
			if (normMap.containsKey(normBuf)) {
				colors[i - 1][j - 1] = normMap.get(normBuf);
				
				continue;
			}
			
			while (true) {
				final long oldNormMod = Math.floorMod(oldNorm, mod);
			
				if (visited.contains(oldNormMod)) {
					happy = -1; // BLACK
				
					break;
				}
						
				long norm = 1, normNoMod;
				boolean modHit = false;
						
				factors = factors(oldNormMod);
				primeFactors.addAll(factors.keySet());
				expFactors.addAll(factors.values());
				preSortExpFactors.addAll(factors.values());
				visited.add(oldNormMod);
						
				Collections.sort(primeFactors);
				Collections.sort(expFactors);
				
				for (int k = 0; k < primeFactors.size(); k++) {
					normNoMod = norm * pow(primeFactors.get(k), expFactors.get(k));
					norm = Math.floorMod(norm * pow(primeFactors.get(k), expFactors.get(k)), mod);
				
					if (normNoMod < norm) {
						modHit = true;
					}
				}
						
				if (norm == 0) {
					happy = -3; // GRAY
					
					break;
				}
					
				if (isPrime(norm)) {
					happy = norm;
				
					break;
				}

				if (preSortExpFactors.equals(expFactors)) {
					happy = -2; // WHITE
					
					break;
				}
						
				if (!modHit) { // mod did not hit -> cheat to get new prime factors
					oldNorm = norm + 1;
					primeFactors.clear();
					expFactors.clear();
					preSortExpFactors.clear();
							
					continue;
				}
							
				oldNorm = norm;
				primeFactors.clear();
				expFactors.clear();
				preSortExpFactors.clear();
			}

			colors[i - 1][j - 1] = happy;
			normMap.put(normBuf, happy);
		}
	});
				
	normMap.clear();
			
	System.out.println(factors(mod));
			
	return getSmoothColors(colors);
}

Java-Code for mode sum

public Color[][] sum(final BiFunction<Long, Long, Long> fun, final long mod) {
	final long[][] colors = new long[pixelWidth][pixelHeight];
	final DoubleAdder progress = new DoubleAdder();
		
	java.util.stream.IntStream.range(1, pixelWidth + 1).parallel().forEach(i -> {
		for(int j = 1; j <= pixelHeight; j++) {
			final List<Long> primeFactors = new ArrayList<>();
			final List<Integer> expFactors = new ArrayList<>(), preSortExpFactors = new ArrayList<>();
			final long normBuf = fun.apply((long)i, (long)j);
			final Set<Long> visited = new HashSet<>();
			Map<Long, Integer> factors;
			long oldNorm = normBuf, happy = 0;
					
			if (normMap.containsKey(normBuf)) {
				colors[i - 1][j - 1] = normMap.get(normBuf);
				
				continue;
			}
					
			while (true) {
				final long oldNormMod = Math.floorMod(oldNorm, mod);
						
				if (visited.contains(oldNormMod)) {
					happy = -1; // BLACK
							
					break;
				}
						
				long norm = 1;
						
				factors = factors(oldNormMod);
				primeFactors.addAll(factors.keySet());
				expFactors.addAll(factors.values());
				preSortExpFactors.addAll(factors.values());
				visited.add(oldNormMod);
						
				Collections.sort(primeFactors);
				Collections.sort(expFactors);
					
				for (int k = 0; k < primeFactors.size(); k++) {
					norm += Math.floorMod(pow(primeFactors.get(k), expFactors.get(k)), mod);
				}
						
				if (norm == 0) {
					happy = -3; // GRAY
							
					break;
				}
					
				if (isPrime(norm)) {
					happy = norm;
					
					break;
				}
						
				if (preSortExpFactors.equals(expFactors)) {
					happy = -2; // WHITE
					
					break;
				}
						
				oldNorm = norm;
				primeFactors.clear();
				expFactors.clear();
				preSortExpFactors.clear();
			}

			colors[i - 1][j - 1] = happy;
			normMap.put(normBuf, happy);
		}
	});
		
	normMap.clear();
		
	System.out.println(factors(mod));
		
	return getSmoothColors(colors);
}

Mode jacobi

This mode calculates the jacobi-symbol norm(x,y)n for pixel (x,y) and fixed (odd) modulus n = p 0 k0 ⋅ p 1 k1 ⋅ … ⋅ p m km
https://en.wikipedia.org/wiki/Jacobi_symbol