Accès libre

Procedural generation of aesthetic patterns from dynamics and iteration processes

À propos de cet article

Citez

Agarwal, R., O’Regan, D. and Sahu, D. (2007). Iterative construction of fixed points of nearly asymptotically nonexpansive mappings, Journal of Nonlinear and Convex Analysis 8(1): 61-79.Search in Google Scholar

Anderson, D. and Wood, Z. (2008). User driven two-dimensional computer-generated ornamentation, in G. Bebis et al. (Eds.), Advances in Visual Computing: 4th International Symposium, ISVC 2008. Proceedings, Part I, Springer, Berlin/Heidelberg, pp. 604-613.10.1007/978-3-540-89639-5_58Search in Google Scholar

Ashish, Rani, M. and Chugh, R. (2014). Julia sets and Mandelbrot sets in Noor orbit, Applied Mathematics and Computation 228: 615-631.10.1016/j.amc.2013.11.077Search in Google Scholar

Chen, Y.-S., Shie, J. and Chen, L.-H. (2012). A NPR system for generating floral patterns based on l-system, Bulletin of Networking, Computing, Systems, and Software 1(1): 38-41.Search in Google Scholar

Chung, K. and Chan, H. (1993). Symmetrical patterns from dynamics, Computer Graphics Forum 12(1): 33-40. 10.1111/1467-8659.1210033Open DOISearch in Google Scholar

Chung, K. and Chan, H. (1995). Spherical symmetries from dynamics, Computers & Mathematics with Applications 29(7): 67-81.10.1016/0898-1221(95)00019-UOpen DOISearch in Google Scholar

Chung, K., Chan, H. and Wang, B. (2001). Tessellations in three-dimensional hyperbolic space from dynamics and the quaternions, Chaos, Solitons & Fractals 12(7): 1181-1197.10.1016/S0960-0779(00)00086-2Open DOISearch in Google Scholar

Ebert, D., Musgrave, F., Peachey, D., Perlin, K. and Worley, S. (2002). Texturing and Modeling: A Procedural Approach, 3rd Edition, Morgan Kaufmann, San Francisco, CA.10.1016/B978-155860848-1/50029-2Search in Google Scholar

Gdawiec, K. (2013). Polynomiography and various convergence tests, in V. Skala (Ed.), WSCG 2013 Communication Papers Proceedings, Vaclav Skala-Union Agency, Plzen, pp. 15-20.Search in Google Scholar

Gdawiec, K. (2017). Inversion fractals and iteration processes in the generation of aesthetic patterns, Computer Graphics Forum 36(1): 35-45.10.1111/cgf.12783Open DOISearch in Google Scholar

Gdawiec, K. and Kotarski, W. (2017). Polynomiography for the polynomial infinity norm via Kalantari’s formula and nonstandard iterations, Applied Mathematics and Computation 307: 17-30.10.1016/j.amc.2017.02.038Search in Google Scholar

Gdawiec, K., Kotarski, W. and Lisowska, A. (2015). Polynomiography based on the non-standard Newton-like root finding methods, Abstract and Applied Analysis 2015, Article ID: 797594.10.1155/2015/797594Search in Google Scholar

Greenfield, G. (2016). Turing-like patterns from cellular automata, in E. Torrence et al. (Eds.), Proceedings of Bridges 2016: Mathematics, Music, Art, Architecture, Education, Culture, Tessellations Publishing, Phoenix, AZ, pp. 151-158.Search in Google Scholar

Horne, C. (2000). Geometric Symmetry in Patterns and Tilings, CRC Press, Boca Raton, FL. Jia, C. and Ming-Xi, T. (2013). Integrating shape grammars into a generative system for Zhuang ethnic embroidery design exploration, Computer-Aided Design 45(3): 591-604.Search in Google Scholar

Kang, S., Alsulami, H., Rafiq, A. and Shahid, A. (2015a). S-iteration scheme and polynomiography, Journal of Nonlinear Science and Applications 8(5): 617-627.10.22436/jnsa.008.05.14Search in Google Scholar

Kang, S., Rafiq, A., Latif, A., Shahid, A. and Kwun, Y. (2015b). Tricorns and multicorns of S-iteration scheme, Journal of Function Spaces 2015, Article ID: 417167.10.1155/2015/417167Search in Google Scholar

Klempien-Hinrichs, R. and von Totth, C. (2010). Generation of Celtic key patterns with tree-based collage grammars, Electronic Communications of the EASST 26: 205-221.Search in Google Scholar

Lalitha, D. and Rangarajan, K. (2012). Petri nets generating Kolam patterns, Indian Journal of Computer Science and Engineering 3(1): 68-74.Search in Google Scholar

Lu, J., Ye, Z. and Zou, Y. (2007). Automatic generation of colorful patterns with wallpaper symmetries from dynamics, The Visual Computer 23(6): 445-449.10.1007/s00371-007-0116-9Open DOISearch in Google Scholar

Lu, J., Zou, Y. and Li, W. (2010). Colorful patterns with discrete planar symmetries from dynamical systems, Fractals 18(1): 35-43.10.1142/S0218348X10004671Open DOISearch in Google Scholar

Lu, J., Zou, Y., Liu, Z. and Li, W. (2012). Colorful symmetric images in three-dimensional space from dynamical systems, Fractals 20(1): 53-60.10.1142/S0218348X12500053Open DOISearch in Google Scholar

Lu, J., Zou, Y., Yang, C. and Wang, L. (2014). Orbit trap rendering methods for generating colorful symmetric images in three-dimensional space, Nonlinear Dynamics 77(4): 1643-1651.10.1007/s11071-014-1406-1Search in Google Scholar

Mann, W. (1953). Mean value methods in iteration, Proceedings of the American Mathematical Society 4(3): 506-510.10.1090/S0002-9939-1953-0054846-3Open DOISearch in Google Scholar

Noor, M. (2000). New approximation schemes for general variational inequalities, Journal of Mathematical Analysis and Applications 251(1): 217-229.10.1006/jmaa.2000.7042Search in Google Scholar

Ouyang, P., Zhao,W. and Huang, X. (2015). Beautiful math. Part 5: Colorful Archimedean tilings from dynamical systems, IEEE Computer Graphics and Applications 35(6): 90-96.Search in Google Scholar

Pickover, C. (2001). Computers, Pattern, Chaos, and Beauty: Graphics from an Unseen World, Dover Publications, Mineola, NY. Search in Google Scholar

Qi, W. and Li, X. (2009). Example-based floral pattern generation, Proceedings of the 5th International Conference on Image and Graphics, Xi’an, Shanxi, China, pp. 553-558.Search in Google Scholar

Sayed, Z., Ugail, H., Palmer, I., Purdy, J. and Reeve, C. (2016). Auto-parameterized shape grammar for constructing Islamic geometric motif-based structures, in M. Gavrilova et al. (Eds.), Transactions on Computational10.1007/978-3-662-53090-0_8Search in Google Scholar

Science XXVIII: Special Issue on Cyberworlds and Cybersecurity, Springer, Berlin/Heidelberg, pp. 146-162.Search in Google Scholar

Setti, R. (2015). Generative dreams from deep belief networks, in C. Soddu and E. Colabella (Eds.), Generative Art 2015: Proceeding of the XVIII Generative Art Conference, Domus Argenia Publisher, Milan, pp. 260-273.Search in Google Scholar

von Gagern, M. and Richter-Gebert, J. (2009). Hyperbolization of Euclidean ornaments, Electronic Journal of Combinatorics 16(2): R12.10.37236/78Search in Google Scholar

Wei, L.-Y., Lefebvre, S., Kwatra, V. and Turk, G. (2009). State of the art in example-based texture synthesis, State of the Art Report: EG-STAR, Eurographics Association, Munich.Search in Google Scholar

Yeh, Y.-T., Breeden, K., Yang, L., Fisher, M. and Hanrahan, P. (2013). Synthesis of tiled patterns using factor graphs, ACM Transactions on Graphics 32(1), Article no. 3.10.1145/2421636.2421639Open DOISearch in Google Scholar

eISSN:
2083-8492
Langue:
Anglais
Périodicité:
4 fois par an
Sujets de la revue:
Mathematics, Applied Mathematics