Peran Matematis Fraktal dalam Analisis Pola Pertumbuhan Tanaman Tropis dan Aplikasinya untuk Optimasi Pertanian Presisi di Era Modern
DOI:
https://doi.org/10.59031/jnts.v1i3.767Keywords:
Agriculture, Fractal Geometry, Growth Patterns, Precision Farming, Tropical PlantsAbstract
The role of fractal geometry in analyzing growth patterns of tropical plants and its application in precision agriculture has become an emerging interdisciplinary topic in the modern era. Tropical plants often exhibit complex and irregular structures that cannot be fully described by conventional Euclidean geometry. This study aims to examine fractal-based mathematical models to identify self-similar patterns in tropical leaves and to explore their potential for optimizing precision farming practices. The methodology employs image-based mathematical analysis, using digital images of tropical plants to measure fractal dimensions and quantify growth complexity. The findings reveal that consistent fractal patterns can be observed across different species of tropical plants, particularly in leaf venation and branching structures, indicating a universal growth principle. Such patterns demonstrate high predictive potential for estimating biomass, monitoring plant health, and assessing responses to environmental changes. Furthermore, the study highlights how fractal-based approaches, when combined with precision agriculture technologies, can improve resource efficiency by supporting accurate irrigation scheduling, soil quality monitoring, and yield forecasting. The implications extend to sustainable agricultural development, as fractal analysis provides a scientific foundation for balancing productivity with environmental preservation. In conclusion, this research underscores the significance of fractals not only as mathematical concepts but also as powerful analytical tools with practical benefits, offering new pathways to advance digital farming, ecological monitoring, and sustainable food security in the modern era.
References
Anderson, S. H. (2011). Fractal analysis of soil structure. In Classification and application of fractals (pp. 137–148).
Aswathy, R. K., & Mathew, S. (2016). On different forms of self-similarity. Chaos, Solitons & Fractals, 87, 102–108. https://doi.org/10.1016/j.chaos.2016.03.021
Azpeitia, E., Tichtinsky, G., Le Masson, M., Serrano-Mislata, A., Lucas, J., Gregis, V., Gimenez, C., Prunet, N., Farcot, E., Kater, M. M., Bradley, D., Madueño, F., Godin, C., & Parcy, F. (2021). Cauliflower fractal forms arise from perturbations of floral gene networks. Science, 373(6551), 192–197. https://doi.org/10.1126/science.abg5999
Bec, J. L., Courbaud, B., Moguédec, G. L., & Pélissier, R. (2015). Characterizing tropical tree species growth strategies: Learning from inter-individual variability and scale invariance. PLoS ONE, 10(3), e0117028. https://doi.org/10.1371/journal.pone.0117028
Bhattacharya, M., & Datta, D. (2023). Mathematics of fractal and its application to study fluid flow and heat transfer of nanofluid through fractal microchannel. AIP Conference Proceedings, 2852(1), 140006. https://doi.org/10.1063/5.0164500
Cai, C., & Wang, P. (2014). Recent progress of research and applications of fractal and its theories in medicine. Journal of Biomedical Engineering, 31(5), 1155–1159.
Carvajal, M. A., Pahari, B. R., & Oates, W. (2023). Finite difference modeling of heat diffusion on diffusion-limited aggregation generated fractal structures. Proceedings of SPIE, 12484, 1248407. https://doi.org/10.1117/12.2658500
Chaturvedi, A., & Prasad, P. R. C. (2013). Application of fractal geometry in determining optimal quadrat size for vegetation sampling. Current Science, 105(9), 1275–1281.
Chery, J. G., Pace, M. R., Acevedo-Rodríguez, P., Specht, C. D., & Rothfels, C. J. (2020). Modifications during early plant development promote the evolution of nature's most complex woods. Current Biology, 30(2), 237–244.e2. https://doi.org/10.1016/j.cub.2019.11.003
Da Silva, E. R. O., Pereira, M. G., de Barros, M. M., dos Santos, L. M. M., & Gomes, J. H. G. (2022). Soil organic matter fractions and multivariate analysis in the definition of pasture management zones. Engenharia Agrícola, 42(6), e20220099. https://doi.org/10.1590/1809-4430-ENG.AGRIC.V42N6E20220099/2022
Di Paola, M., Russotto, S., & Pirrotta, A. (2022). Self-similarity and response of fractional differential equations under white noise input. Probabilistic Engineering Mechanics, 70, 103327. https://doi.org/10.1016/j.probengmech.2022.103327
Grizzi, F., Spadaccini, M., Chiriva-Internati, M., Hegazi, M. A. A. A., Bresalier, R. S., Hassan, C., Repici, A., & Carrara, S. (2023). Fractal nature of human gastrointestinal system: Exploring a new era. World Journal of Gastroenterology, 29(25), 4036–4052. https://doi.org/10.3748/wjg.v29.i25.4036
Hassan, M. K. (2019). Is there always a conservation law behind the emergence of fractal and multifractal? European Physical Journal Special Topics, 228(1), 209–232. https://doi.org/10.1140/epjst/e2019-800110-x
Ji, Z., Card, K. J., & Dazzo, F. B. (2015). CMEIAS JFrad: A digital computing tool to discriminate the fractal geometry of landscape architectures and spatial patterns of individual cells in microbial biofilms. Microbial Ecology, 69(3), 710–720. https://doi.org/10.1007/s00248-014-0495-1
Kalck, A. S., Pedro, M. F. C., dos Santos, K. F., Sousa, M. S., Silva, J. R., & de Souza, N. C. (2018). Mathematical models and fractal analysis for the investigation of the photodynamic inactivation in phytopathogenic microorganisms. Colloids and Surfaces B: Biointerfaces, 171, 285–290. https://doi.org/10.1016/j.colsurfb.2018.07.019
Karamchedu, C. D. (2016). Use of fractal dimension ratios of plant images as an allometric predictor of plant biomass. 2016 IEEE International Geoscience and Remote Sensing Symposium (IGARSS), 1352–1355. https://doi.org/10.1109/IGARSS.2016.7729344
Ma, X., Wu, Y., Shen, J., Duan, L., & Liu, Y. (2021). Ml-lme: A plant growth situation analysis model using the hierarchical effect of fractal dimension. Mathematics, 9(12), 1322. https://doi.org/10.3390/math9121322
Muraleedharan, V., Rajan, S. C., & R, J. (2023). Determining the limits of traditional box-counting fractal analysis in leaf complexity studies. Flora, 304, 152300. https://doi.org/10.1016/j.flora.2023.152300
Nelissen, H., & Gonzalez, N. (2020). Understanding plant organ growth: A multidisciplinary field. Journal of Experimental Botany, 71(1), 7–10. https://doi.org/10.1093/jxb/erz448
Niralda, P. C., & Mathew, S. (2022). On properties of similarity boundary of attractors in product dynamical systems. Discrete and Continuous Dynamical Systems – Series S, 15(2), 265–281. https://doi.org/10.3934/dcdss.2021004
Niralda, P. C., Mathew, S., & Secelean, N. A. (2021). On boundaries of attractors in dynamical systems. Communications in Nonlinear Science and Numerical Simulation, 94, 105572. https://doi.org/10.1016/j.cnsns.2020.105572
Nugroho, A. P., Sutiarso, L., & Okayasu, T. (2019). Appropriate adaptation of precision agriculture technology in open field cultivation in tropics. IOP Conference Series: Earth and Environmental Science, 355(1), 012028. https://doi.org/10.1088/1755-1315/355/1/012028
Padhy, R., Biswal, S., Dash, S. K., & Mishra, J. (2022). Fractal-based soil assessment to obtain precision agriculture using machine learning approach. In Lecture Notes in Networks and Systems (Vol. 431, pp. 417–434). Springer. https://doi.org/10.1007/978-981-19-0901-6_38
Yakushev, V. P., Kanash, E. V., Yakushev, V. V., Matveenko, D. A., Rusakov, D. V., Blokhina, S. Y., Petrushin, A. F., & Mitrofanov, E. P. (2019). Advanced features of automated detection of within-field variability based on hyperspectral images and optical criteria. Sovremennye Problemy Distantsionnogo Zondirovaniya Zemli iz Kosmosa, 16(3), 24–32. https://doi.org/10.21046/2070-7401-2019-16-3-24-32
Zhang, Y., Yu, J., He, H., Wang, J., & Yang, X. (2019). Research on fractal characteristics of building energy consumption time series. IOP Conference Series: Earth and Environmental Science, 242(6), 062038. https://doi.org/10.1088/1755-1315/242/6/062038
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