Journal of Korea Game Society (한국게임학회 논문지)

Korea Game Society (한국게임학회)
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Creation of Fractal Images with Rotational Symmetry Based on Julia Set

Julia Set을 이용한 회전 대칭 프랙탈 이미지 생성

  • 한영덕 (우석대학교 정보보안학과)
  • Received : 2014.11.24
  • Accepted : 2014.12.10
  • Published : 2014.12.20
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Abstract

We studied the creation of fractal images with polygonal rotation symmetry. As in Loocke's method[13] we start with IFS of affine functions that create polygonal fractals and extends the IFS by adding functions that create Julia sets instead of adding square root functions. The resulting images are rotationally symmetric and Julia set shaped. Also we can improve fractal images by modifying probabilistic IFS algorithm, and we suggest a method of deforming Julia set by changing exponent value.

이미지 디자인 등에 사용하기에 용이한 정다각형의 회전대칭성을 갖는 프랙탈 생성에 대해 연구하였다. Loocke의 논문[13]에서 사용한 방법과 같이 회전, 축소 아핀함수를 기반으로 하되 제곱근(square root)함수 대신 줄리아 셋(Julia set)을 생성하는 함수들로 확장하여 IFS(iterated function systems)를 구성하였다. 그 결과 줄리아 셋의 모양에 바탕을 둔 회전 대칭적 프랙탈을 생성할 수 있었으며, 줄리아 셋의 모양이 잘 나타나지 않는 경우에는 IFS 생성 알고리즘의 확률적 함수선택 부분을 변경하여 줄리아 셋의 모양이 뚜렸해지도록 할 수 있음을 보였다. 또한 줄리아 셋의 모양을 지수의 변화를 통해 변형하는 방법을 제안하였다.

Keywords

References

  1. Barnsley M. "Fractals everywhere", 2nd ed. New York: Academic Press Professional, 1993.
  2. Hang-Sook Song, Young-Duk Han, "A Study of Fractal Object Deformation for Game Environment", Journal of Korea Game Society, Vol.5, No.1, pp.19-24, 2005.
  3. Jeong-Jin Lee, Moon-Koo Kang, "3D Cloud Animation using Cloud Modeling Method of 2D Meteorological Satellite Images", Journal of Korea Game Society, Vol.10, No.1, pp.147-156, 2010.
  4. Young Cheul Wee, "A Very Fast 2*2 Fractal Coding by Spatial Prediction", Journal of KIISE:Computer Systems and Theory, Vol. 31, No. 11, pp.611-616, 2004.
  5. Jaehong Park, Cheolwoo Park, Wonseok Yang, "Fractal Image Coding for Improve the Quality of Medical Images", J. Korean. Soc. Radiol., Vol. 8, No. 1, January 2014. https://doi.org/10.7742/jksr.2014.8.1.19
  6. Jin-Mo Kim, Hyung-Je Cho, "Real time Rendering of Realistic Grasses Using Fractal and Shader-Instancing", J. Korea Multimedia Soc. Vol. 13, No. 2, pp.298-307, Feb. 2010.
  7. Atin Das, Pritha Das, "Fractal analysis of songs: Performer's preference", Nonlinear Analysis: Real World Applications Vol. 11, Iss. 3, pp. 1790-1794, 2010. https://doi.org/10.1016/j.nonrwa.2009.04.004
  8. Scott Draves, "The Fractal Flame Algorithm", 1992.
  9. Field M, Golubitsky M. Symmetry in Chaos. New York:Oxford University Press, 1992.
  10. Brisson G, Gartz K, McCune B, O'Brien K, Reiter C, Symmetric attracters in three-dimensional space, Chaos Solitons and Fractal Vol.7, Iss. 7, pp. 1033-51. 1996. https://doi.org/10.1016/0960-0779(95)00094-1
  11. Reiter C, Chaotic attracters with the symmetry of the dodecahedron. The Visual Computer, Vol. 15, Iss. 4, pp. 211-5, 1999. https://doi.org/10.1007/s003710050173
  12. Kevin C. Jones, Clifford A. Reiter, "Chaotic attractors with cyclic symmetry revisited", Computers & Graphics Vol. 24, Iss. 2, pp. 271-282, 2000. https://doi.org/10.1016/S0097-8493(99)00161-2
  13. Philip Van Loocke, "Non-linear iterated function systems and the creation of fractal patterns over regular polygons", Computers & Graphics Vol. 33, Iss. 6, pp. 698-704, 2009. https://doi.org/10.1016/j.cag.2009.05.003