Trees continue to fascinate with their natural beauty and as engineering masterpieces optimal with respect to several independent criteria. Pythagorean tree is a well-known fractal design that realistically mimics the natural tree branching structures. We study various types of Pythagorean-like fractal trees with different shapes of the base, branching angles and relaxed scales in an attempt to identify and explain which variants are the closest match to the branching structures commonly observed in the natural world. Pursuing simultaneously the realism and minimalism of the fractal tree model, we have developed a flexibly parameterised and fast algorithm to grow and visually examine deep Pythagorean-inspired fractal trees with the capability to orderly over- or underestimate the Leonardo da Vinci's tree branching rule as well as control various imbalances and branching angles. We tested the realism of the generated fractal tree images by means of the classification accuracy of detecting natural tree with the transfer-trained deep Convolutional Neural Networks (CNNs). Having empirically established the parameters of the fractal trees that maximize the CNN's natural tree class classification accuracy we have translated them back to the scales and angles of branches and came to the interesting conclusions that support the da Vinci branching rule and golden ratio based scaling for both the shape of the branch and imbalance between the child branches, and claim the flexibly parameterized fractal trees can be used to generate artificial examples to train robust detectors of different species of trees.

本研究解决了自然界树木分支结构重建的真实性与简约性之间的矛盾，提出了一种灵活参数化的快速算法，能够模拟不同形状和分支角度的毕达哥拉斯类似分形树。通过使用深度卷积神经网络检测自然树的分类准确性，本研究发现这些分形树的参数能显著支持达芬奇的分支规则和黄金比例，从而为不同树种的检测器训练提供了有效的人工样本生成方法。

列奥纳多的辩护：用于最小重构自然分支结构的毕达哥拉斯树