Xuening Tang1, Dongxing Yu2,*, Jinhai Yan3
1University of Amsterdam, Amsterdam, the Netherlands.
2School of Education, Sanda University, Shanghai, China.
3Division of Applied Mathematics, School of Mathematical Sciences, Fudan University, Shanghai, China.
*Corresponding author:Dongxing Yu
References
[1] Barnsley, M. F. (1988). Fractals everywhere. https://dl.acm.org/citation.cfm?id=59931
[2] Bates, T. (2019). A generalization of the chaos game. Bridges 2019 Conference Proceedings, 139-146. http://archive.bridgesmathart.org/2019/bridges2019-139.pdf.
[3] Schlicker, S., & Dennis, K. (1995). Sierpinski n-gons. Pi Mu Epsilon Journal, 10(2), 81-89.
[4] Karplus, A. (2008). Self-similar Sierpinski Fractals. Science Fair.
[5] Kahng, B., & Davis, J. (2010). Maximal dimensions of uniform Sierpinski fractals. Fractals, 18(04), 451-460.
https://doi.org/10.1142/s0218348x10005135.
[6] Tzanov, V. (2015). Strictly self-similar fractals composed of star-polygons that are attractors of Iterated Function Systems. arXiv (Cornell University). http://export.arxiv.org/pdf/1502.01384.
[7] Shynkarenko, V. (2019). Constructive-Synthesizing representation of geometric fractals. Cybernetics and Systems Analysis, 55(2), 186–199. https://doi.org/10.1007/s10559-019-00123-w.
[8] Puglisi, G., & Pugno, N. (2022). A new concept for superior energy dissipation in hierarchical materials and structures. International Journal of Engineering Science, 176, 103673. https://doi.org/10.1016/j.ijengsci.2022.103673.
[9] Zhang, X., Li, R., Li, N., Gu, G., Zhang, Y., Hou, S., & Wang, Y. (2018). Sierpiński triangles formed by molecules with linear backbones on Au(111). Chinese Chemical Letters, 29(6), 967-969. https://doi.org/10.1016/j.cclet.2017.09.041.
[10] Rian, I. M. (2022). Fractal-based algorithmic design of Chinese ice-ray lattices. Frontiers of Architectural Research, 11(2), 324-339. https://doi.org/10.1016/j.foar.2021.10.010.
[11] Zhou, H., & Dong., S. Y. (2018). The enlightenment of "Sherbinski Carpet" fractal theory to modern city structure. Chinese & Oversees Architecture.
[12] Husain, A., Reddy, J., Bisht, D., & Sajid, M. (2021). Fractal dimension of coastline of Australia. Scientific Reports (Nature Publishing Group), 11(1). https://doi.org/10.1038/s41598-021-85405-0.
[13] Casnedi, L., Licheri, R., Brun, M., & Pia, G. (2020). From nature geometry to material design: Advanced fractal nature analysis for predicting experimental elastic properties. Ceramics International, 46(15), 23947–23955. https://doi.org/10.1016/j.ceramint.2020.06.171.
[14] Mandelbrot, B. B. (1983). The fractal geometry of nature. Macmillan.