CUDA implementation for Julia set computation.

In this project we:

• Generate the Julia set on the GPU by dividing the work load in a 2D thread configuration.
• Evaluate the correctness of generated results by comparing the generated images.
• Compare the GPU vs CPU execution time as a function of image size for a given value of c.

Julia sets are a type of fractals that can be computed in the complex domain. The Julia set is associated with points z = x + iy on the complex plane for which the series

z_n+1 = z_n² + c,

does not tend to infinity. Here, c is a complex constant, and one gets a different Julia set for each c. The initial value z₀ for the series is each point in the image plane. In order to compute the Julia set, we need to determine if a point escapes to infinity under the given mapping or remains bounded in the image plane.

Here we introduce a color coding that is proportional to the number of iterations taken by a point to escape a circle of radius 2 units (a heuristic for escape to infinity).

1. Correctness:

   • Images produced by CPU and GPU (for N = 4096)

     CPU Image	GPU Image

   • Percentage similarity and the average error in pixel values as a function of N.

     Image side length (N)	Percentage Similarity	Average Error
     256	99.970505	0.003031
     512	99.97406	0.00266
     1024	99.969864	0.003068
     2048	99.970039	0.003168
     4096	99.969704	0.003297

2. Execution time comparision (with c = 0.285 + i 0.01):

   

   Image side length (N)	CPU (ms)	GPU {Kernel + Memory Transfer} (ms)
   256	49.796	0.295808
   512	194.068	0.55424
   1024	769.479	1.475488
   2048	3083.295	4.24192
   4096	12297.033	15.2028160

• Run make and set the library path: export LD_LIBRARY_PATH=./devil/lib.
• Execute the object file created, ./parallel_julia.