论文标题
高海高吉曲线和$β$ -CANTOR功能从机械定律
The Takagi Curve and the $β$-Cantor Function from Mechanical Laws
论文作者
论文摘要
这项工作表明，可以从机械定律中获得分形，而不会被任何算法强迫，从而缩小了数学和自然的柏拉图式世界之间的差距。将弹性理论应用于二元树的分支应力时，分形树冠直接出现。节点的垂直位移是由高加壁曲线给出的，而水平曲线的垂直位移是通过$β$ - cantor函数的媒介函数的线性组合给出的。此外，两个分形维度都是相关的，这表明高吉曲线与$β$ - cantor函数之间的更深层次的联系。
This work shows that fractals can be obtained from Mechanical Laws without being forced by any algorithm, closing the gap between the Platonic world of Mathematics and Nature. Fractal tree crown directly emerges when applying elasticity theory to branching stresses in a binary tree. Vertical displacements of nodes are given by the Takagi curve, while the horizontal ones are given by a linear combination of inverses of $β$-Cantor functions. In addition, both fractal dimensions are related, which suggests a deeper connection between the Takagi Curve and the $β$-Cantor function.
