Fractals are self-similar objects with fractal dimensions. Algebraic fractals are generated with large number of iterations of specific formula where exit expression becomes a new entrance to equation. The numbers that we are trying to qualify in Escape or Prisoner set can diverge or converge in a big number of iterations. If they converge they belong to Prisoner set and if they diverge they belong to Escape set. Limit of those two sets has fractal dimension. If complex constant c for Julia belongs to Mandelbrot set, attractors for Julia can be calculated. In this paper, we calculate do those attractors appeal Julia sets. If they do, they belong to Mandelbrot. That is how we design our Mandelbrot set. We also demonstrate that Julia set for which we know how to calculate attractors has one attractor (found on x-axis) of absolute value smaller than one. Because of the enormous size of the data problem is solved through parallel programing with OpenCL. GPU is used as an accelerator because it has many compute units and each one of them consists of multiple SIMD vector unit. On every compute unit in one cycle one work group completes one operation. Work group shares local memory. GPU has control on every work item through its global ID. We run same operations (kernel) on all data within a set. We create kernel after we have established communication with platform, with device, after we have created context and linked it with device, after we have created command queue and linked it with context and with the device, created CL program, linked it with the device, context and compiled it. Kernel starts execution when it’s linked with the command queue. After all the data is done we can write the exit in the argument that we set as a pointer (and specify with write flag) when we started kernel execution. With this approach, we have accelerated the process of solving this complex assignment.