Implementation and Analysis of Fractals Shapes using GPU-CUDA Model

Authors

  • Amira Bibo Sallow Department of Computer Science, Nawroz University, Duhok, Kurdistan Region - Iraq

DOI:

https://doi.org/10.25007/ajnu.v10n2a1030

Keywords:

Fractal, Fractal Shapes, Mandelbrot & Julia Set, Self-Similar, GPU, Speedup.

Abstract

The rapid evolution of floating-point computing capacity and memory in recent years has resulted graphics processing units (GPUs) an increasingly attractive platform to speed scientific applications and are popular rapidly due to the large amount of data that processes the data on time. Fractals have many implementations that involve faster computation and massive amounts of floating-point computation. In this paper, constructing the fractal image algorithm has been implemented both sequential and parallel versions using fractal Mandelbrot and Julia sets. CPU was used for the execution in sequential mode while GPUarray and CUDA kernel was used for the parallel mode. The evaluation of the performance of the constructed algorithms for sequential structure using CPUs (2.20 GHz and 2.60 GHz) and parallelism structure for various models of GPU (GeForce GTX 1060 and GeForce GTX 1660 Ti ) devices, calculated in terms of execution time and speedup to compare between CPU and GPU maximum ability. The results showed that the execution on GPU using GPUArray or GUDA kernel is faster than its sequential implementation using CPU. And the execution using the GUDA kernel is faster than the execution using GPUArray, and the execution time between GPU devices was different, GPU with (Ti) series execute faster than the other models.

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References

1. Anthony Atella. (2018). Rendering Hypercomplex Fractals. Honors Projects Overview, 44.
2. Belma, A., & Sonay, A. (2016). Fractals and Fractal Design in Architecture. 17(3), 10.
3. Biswas, H. R., Hasan, M., & Bala, S. K. (2018). CHAOS THEORY AND ITS APPLICATIONS IN OUR REAL LIFE. 19.
4. Divya Udayan J. (2013). Fractal Based Method on Hardware Acceleration for Natural Environments. Future Technology Research Association International, 4(3).
5. Haji, L. M., Zebari, R. R., Zeebaree, S. R. M., Mustafa, W., Shukur, H. M., & Ahmed, O. M. (2020). GPUs Impact on Parallel Shared Memory Systems Performance. 24(08), 9.
6. Hungilo, G. G., Emmanuel, G., & Pranowo. (2020). Performance comparison in simulation of Mandelbrot set fractals using Numba. 030007. https://doi.org/10.1063/5.0000636
7. Jimenez, L. I., Sanchez, S., Martan, G., Plaza, J., & Plaza, A. J. (2017). Parallel Implementation of Spatial–Spectral Endmember Extraction on Graphic Processing Units. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 10(4), 1247–1255. https://doi.org/10.1109/JSTARS.2016.2645718
8. Kirk, D., & Hwu, W. (2017). Programming massively parallel processors: A hands-on approach (Third edition). Elsevier.
9. Kirk, D., & Hwu, W. W. (2013). Programming massively parallel processors: A hands-on approach (2. ed). Elsevier, Morgan Kaufmann.
10. Liu, Y., Cui, H., & Zhao, R. (2019). Fast Acquisition of Spread Spectrum Signals Using Multiple GPUs. IEEE Transactions on Aerospace and Electronic Systems, 55(6), 3117–3125. https://doi.org/10.1109/TAES.2019.2902695
11. Mandelbrot, B. B. (1982). The fractal geometry of nature. W.H. Freeman.
12. Mandelbrot, B. B. (2004). Fractals and Chaos. Springer New York. https://doi.org/10.1007/978-1-4757-4017-2
13. Negi, A., Garg, A., & Agrawal, A. (2014). A Review on Natural Phenomenon of Fractal Geometry. International Journal of Computer Applications, 86(4), 1–7. https://doi.org/10.5120/14970-3157
14. Nogues, O. C. i, Pascual, D., Onrubia, R., & Camps, A. (2020). Advanced GNSS-R Signals Processing With GPUs. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 13, 1158–1163. https://doi.org/10.1109/JSTARS.2020.2975109
15. Razian, S. A., & Mahvash Mohammadi, H. (2017). Optimizing Raytracing Algorithm Using CUDA. Italian Journal of Science & Engineering, 1(3), 167–178. https://doi.org/10.28991/ijse-01119
16. Sallow, A., & Abdullah, D. (2014). Constructing Sierpinski Gasket Using GPUs Arrays. International Journal of Computer Science Issues, 11(6), 3.
17. Sawant, V. G. (n.d.). DESIGN OF HIGH GAIN FRACTAL ANTENNA. 6(1), 8.
18. Wang, G., Zomaya, A., Martinez, G., & Li, K. (Eds.). (2015). Algorithms and Architectures for Parallel Processing: 15th International Conference, ICA3PP 2015, Zhangjiajie, China, November 18-20, 2015, Proceedings, Part I (Vol. 9528). Springer International Publishing. https://doi.org/10.1007/978-3-319-27119-4
19. Xiaodong Liu, Mo Li, Shanshan Li, Shaoliang Peng, Xiangke Liao, & Xiaopei Lu. (2014). IMGPU: GPU-Accelerated Influence Maximization in Large-Scale Social Networks. IEEE Transactions on Parallel and Distributed Systems, 25(1), 136–145. https://doi.org/10.1109/TPDS.2013.41
20. Zhang, X., & Xu, Z. (2011). Implementation of Mandelbrot set and Julia Set on SOPC platform. 2011 International Conference on Electronics, Communications and Control (ICECC), 1494–1498. https://doi.org/10.1109/ICECC.2011.6066355

Published

2021-04-28

How to Cite

Sallow, A. B. (2021). Implementation and Analysis of Fractals Shapes using GPU-CUDA Model. Academic Journal of Nawroz University, 10(2), 1–10. https://doi.org/10.25007/ajnu.v10n2a1030

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