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Javier Rodríguez-Cuadrado

Publications and source records attributed to Javier Rodríguez-Cuadrado.

2 recordsLinked to original sources

Quasi-Sierpinski Structure for Uniform Load Distribution

Land reclamation methods, indispensable for the proper development of modern coastal cities, are ecologically destructive. We present a fractal structure, similar to a Sierpinski triangle, which solves this problem by resting directly on the seabed thanks to the uniform load distribution we achieve on its base. To obtain this uniform distribution, we show that the supports of the structure must displace vertically following any function of the Takagi class. This causes the vertical deformations of the structure to follow this same class and the horizontal deformations to be related to the Cantor function. The structure works with an unlimited number of combinations of areas of its elements and materials, which gives designers a high degree of constructive flexibility.

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The Takagi Curve and the $β$-Cantor Function from Mechanical Laws

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.

math.DS↗