Fibonacci Solar Trees: supplementary material

Published: 4 March 2024| Version 1 | DOI: 10.17632/3r8kr5p5zd.1


This is the supplementary material of the paper "Fibonacci solar trees", by Grassi, L. B. et al, which brings all material required to verify the results and analyses, and to reproduce the paper, in addition to the source files to build other Fibonacci solar trees according to the user's criteria, and the results of simulations and analysis of a large set of those trees. More specifically, it contains: 1. The code for obtaining Fibonacci coordinates in Python; 2. The models for construction of the Fibonacci tree in Rhinoceros Software and the Grasshopper plug-in, allowing one to change its constructive variables and obtain the incidence value through simulation; 3. The code for obtaining the average annual solar incidence equation coefficients; 4. The code for the graphs and surfaces used for analysis, developed in Matlab software; 5. Data from simulations of the configurable Fibonacci solar tree analyzed over one year for each tree configuration (presented in an spreadsheet), as well as the estimated values, the error between the simulated and estimated incidences; 6. The graphs and surfaces used for analysis (.eps and .png), whether to obtain the incidence equation or to compare the simulated and estimated incidences.


Steps to reproduce

The coordinates of the Fibonacci points are obtained from the code in the file "". These coordinates are used to position the leaves in the tree's construction, where it is possible to obtain several tree instances, varying the leaf area, the projection radius, the internode height, and the number of leaves. The source files for the tree construction are available in the folder called "Configurable_n-leaf_Fibonacci_Tree", containing the leaf model file in .dm, and the tree construction for each number of leaves, in .gh. In the Grasshopper files, the structure of the tree is automated; click on "Data Recorder (Rec)" to start changing the constructive variables and changing the "_run" entry in the "DirectSunHours" box to "True" to obtain the value of simulation of the average annual solar incidence for each instance of the tree. Remember that the Ladybug and Radiance plug-ins must be installed to simulate the incidence. The coefficients are estimated using the "fminunc" function of the Matlab software, whose code is found in the "data_tree_xywk_E.m" file and has as input the constructive variables and the incidence values simulated in the Rhinoceros software. The results of the simulated incidences obtained by the equation, the error between them, as well as the values of the functions g(a,n,r) and f(k,a,n,r) and the daily irradiation, are presented in the table in the file " Fibonacci_Solar_Tree_Simulations.xlsx", for each tree instance, changing the leaf area, projection radius, internode height and the number of leaves. Finally, the graphs for analyzing the incidence behavior as a function of construction variables, the graphs and surfaces comparing the equation and simulated incidences can be reproduced using the code "graphics.m" and "Surfaces.m".


Universidade Federal do Espirito Santo


Applied Mathematics, Solar Energy, Photovoltaics, Computer Simulation


Coordenação de Aperfeiçoamento de Pessoal de Nível Superior

Conselho Nacional de Desenvolvimento Científico e Tecnológico

Fundação de Amparo à Pesquisa e Inovação do Espírito Santo

Secretaria da Ciência, Tecnologia, Inovação, Educação Profissional e Desenvolvimento Econômico of Espírito Santo