Julia set c++ colours - c++

Question

I'm currently working on an assignment where I have to produce a Julia set in C++ in sequential, parallel and OpenCL. I have managed to produce an image but the way I have used colours is very ineffective any ideas on how I could improve the colour section of my code at the moment? below is the sequential section of my code any help in improving how I have set the colours would be much appreciated
void sequentialJulia(const complex<float> C, const UINT size = 1000,
const UINT MAX_ITERATIONS = 100, const float limit = 1.7f) {
int start_s = clock();// starts the timer
// Setup output image
fipImage outputImage;
outputImage = fipImage(FIT_BITMAP, size, size, 24);
UINT bytesPerElement = 3;
BYTE* outputBuffer = outputImage.accessPixels();
vector<int> colors{ 100, 140, 180, 220, 225 };// this sets the intsity of the image, if i was to remove 225 the image would be darker
//vector<int> colors{9, 19, 29, 39, 49 }; //THIS DOESNT WORK DO NOT UNCOMMENT
//RGBQUAD color;
complex<float> Z;
std::cout << "Processing...\n";
for (UINT y = 0; y < size; y++) {
//tracking progress;
cout << y * 100 / size << "%\r";
cout.flush();
for (UINT x = 0; x < size; x++) {
Z = complex<float>(-limit + 2.0f * limit / size * x, -limit + 2.0f * limit / size * y);
UINT i;
for (i = 0; i < MAX_ITERATIONS; i++) {
Z = Z * Z + C;
if (abs(Z) > 2.0f) break;
}
if (i < MAX_ITERATIONS ) { //only changing red byte
// bytes per element 9 = blue
// bytes per element 2 = red
// bytes per element 7 = green
outputBuffer[( y * size + x) * bytesPerElement + 9] = colors[i % 5];
}
}
}
cout << "Saving image...\n";
ostringstream name;
name << "..\\Images\\" << C << " size=" << size << " mIterations=" << MAX_ITERATIONS << " sequential19.png" ;
cout << "saving in: " << name.str().c_str() << "\n";
outputImage.save(name.str().c_str());
cout << "...done\n\n";
int stop_s = clock();
cout << "time: " << (stop_s - start_s) / double(CLOCKS_PER_SEC) * 1000 << endl;// stops the timer once code has executed
}

Answer 1

As far as I remember, fractal generators from the early 90's (e.g.: Fractint) used the iteration-bailout index as an index into a table of 256 Red-Green-Blue colours (This was a common limit, as most displays back then were limited to a colour palette of this size anyway.)
So maybe you could define a table of RGB-colours, then lookup on these up exactly how you perform the colors[i % 5]; now, except it would output a RGB-triple of colours[i % TABLE_SIZE].red, .green, .blue. I think it would be best to load your palette in from a separate file.
I've always wondered what a fractal with a 1000-entry colour palette might look like. Quite pretty I think.
EDIT: IIRC Fractint had a palette editing mode, and could save them to files.

Answer 2

In addition to the excellent idea of using a look-up table, you can also interpolate between values in the table instead of just doing a modulus operation to pick one. So you could have a 5-color look-up table, but apply it to hundreds or thousands of iterations by linearly interpolating between the 5 colors. For example, if you have a maximum iteration of 256 and your current calculation takes 168 iterations to escape to infinity, and you have a 5-color look-up table, you could do this to get a color:
float lookupVal = static_cast<float>((colors.size - 1) * i) / MAX_ITERATIONS;
int lookupIndex = static_cast<int>(floor(lookupValue));
float fraction = lookupVal - floor(lookupVal);
float colorF = static_cast<float>(colors [ lookupIndex ]) + fraction * static_cast<float>(colors [ lookupIndex + 1 ] - colors [ lookupIndex ]);
uint8_t color = static_cast<uint8_t>(colorF);
If your look-up table had RGB values instead of just grayscale, you would need to calculate colorF and color for each color channel (red, green, and blue).