Due: Thursday May 7, 2020 (emailed by 11:59:59 p.m.)

NOTE: This due date is the day before Stop Day. No late submissions will be accepted. As stated in the Syllabus, no project will be accepted under any conditions after this date.

Update for Macintosh Developers

For the ImageWriter library to be seen and used, you must execute the following once per terminal window. (Or just put it in your startup script.):

The Project

In this project, you will use a GPU program to compute images of Mandelbrot and Julia sets. You are free to use either CUDA or OpenCL.

Background

Complex numbers

A complex number can be written as (a + b*i), where i = sqrt(-1). Arithmetic operations involving complex numbers include:

• Adding two complex numbers: (a + b*i) + (c + d*i) = (a + c) + (b + d)*i
• Multiplying two complex numbers: (a + b*i) * (c + d*i) = (a*c - b*d) + (a*d + b*c)*i
• LengthSquared(a + b*i) = (a*a + b*b)

Mandelbrot and Julia Sets, Part 1

Assume the parameters R and S below are complex numbers – R=(a + b*i) and S=(c + d*i) – and consider the following algorithm:

Algorithm ComputeColor(R, S)
LOOP a maximum of MaxIterations times:
{
    X = R2 + S
    if (LengthSquared(X) > MaxLengthSquared)
        break;
    R = X
}
if (MaxIterations was reached)
    color = COLOR_1
else
{
    f = actualNumberIterations/MaxIterations; // 0 < f < 1
    color = (1.0 - f)*COLOR_2 + f*COLOR_3
}
return color
end Algorithm

Color

Colors are 3-tuples: (r, g, b), where each of the three values are fractions between 0 and 1. For example, (1, 1, 0) is a bright yellow; (0, 0.5, 0.5) is a darkish cyan.

Mandelbrot and Julia Sets, Part 2

Mandelbrot and Julia sets are computed point by point in the complex plane. When creating images, we associate each pixel with a point in the complex plane. Thus, for each pixel, we use Algorithm ComputeColor to determine a color for that pixel. This requires us to be able to associate a point in the complex plane with a given pixel. We do that as described next.

We will create images of size nRows x nCols of pixels. Row and column pixel indices will vary 0≤row<nRows; 0≤col<nCols. We will be given a range of the complex plane over which we want to create the fractal: realMin, realMax, imagMin, imagMax. To compute a color for the pixel in (row, col), we compute the complex point:

In a given execution of your program, you will compute either the Mandelbrot set or the Julia set:

• The color for the Mandelbrot set for the current (row, col) position is ComputeColor(Q, Q).
• The color for the Julia set for the current (row, col) position is ComputeColor(Q, J), where the complex number J is another parameter.

To summarize the parameters along with suitable testing values and expected results:

Parameter	Try this value when testing	Approximate Results if Mandelbrot	Approximate Results if Julia
nRows	500
nCols	500
MaxIterations	50
MaxLengthSquared	4
realMin	-1.95
realMax	0.55
imagMin	-1.25
imagMax	1.25
JuliaPoint, J	-0.765 + 0.11*i
COLOR_1	(0, 0, 0)
COLOR_2	(1, 0, 0)
COLOR_3	(1, 1, 0)	"Approximate" largely because the region should be square (500x500), and the images may not be centered inside.

Project Requirements

All the fractal computations will be done in GPU code. The CPU code will be launched as either:

The 'M' or 'J' indicates whether you are computing the Mandelbrot or Julia set. The params file contains the parameters to be used for the current run. (Read and ignore the JuliaPoint if you are computing Mandelbrot.) The final parameter is the image file to create using the ImageWriter utility described below.

A test file with the values suggested in the table above is here. Once you get the project working, you should certainly experiment with other values. It's sort of fun. But don't change too many things at once, and start by making small changes. Fractals have a nasty habit of producing uninteresting images for many parameter settings. Try zooming in on regions that look interesting by shrinking the realMin-realMax and imagMin-imagMax ranges. I will certainly test with other values when grading your submissions.

Computational Grid Configuration

Review the Work Grid Size Determination web page we examined in class. Use the ideas summarized there when determining how to structure your grid (1D, 2D, 3D; sizes in the dimensions; etc.). If you are using OpenCL, you must establish a local work size; do not pass nullptr for that when invoking clEnqueueNDRangeKernel.

ImageWriter Utility

Download Project3Material.tar.gz and uncompress it. This will produce a directory with the following structure:

• ImageWriter: A directory with classes that can open and write an image file in any of jpeg, png, bmp, or tga formats.
• Packed3DArray: A templated data type used by the ImageWriter class to hold an internal frame buffer representation of the image and allow it to be read or written almost as if it were an ordinary 3D array.
• lib: an empty directory into which the ImageWriter compiled library will be stored.
• example: This directory has a simple example program to illustrate how the ImageWriter class can be used. There is also note in it relevant to how the buffers you create and bring back to the CPU should be declared. (There are also a couple sample test programs in the ImageWriter directory itself.) The comments in the header files ImageWriter/ImageWriter.h and Packed3DArray/Packed3DArray.h have extensive documentation on usage as well.

  To run the example program, simply type "make" in the example directory, then launch the program with a command line something like:

  ./example 500 200 1 1 0 MyImage.png

When implementing this project, create another directory as a sibling to ImageWriter, et al. called project3. Put all your project 3 code in there. Do not copy any of the utility code I have given you into your project3 directory. The Makefile in your project3 directory will need lines like those in this portion of a Makefile.

When you submit your project, tar and submit only the project3 subdirectory.

Project Submission

Remove any object files (i.e., *.o) and your linked executable program. Then create and send a tar file of the project3 directory to me at jrmiller@ku.edu.