相关论文: Comment concerning Leonardo's rule

Examining botanical trees, Leonardo da Vinci noted that the total cross-section of branches is conserved across branching nodes. In this Letter, it is proposed that this rule is a consequence of the tree skeleton having a self-similar…

More than five hundred years ago Leonardo Da Vinci found a pattern in the growth of trees nowadays known as the Leonardo's rule. This rule relates the thickness of the stem with the thickness of the branches at different bifurcation stages…

Trees in works of art have stirred emotions in viewers for millennia. Leonardo da Vinci described geometric proportions in trees to provide both guidelines for painting and insights into tree form and function. Da Vinci's Rule of trees…

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…

We study the percolative properties of bi-dimensional systems generated by a random sequential adsorption of line-segments on a square lattice. As the segment length grows, the percolation threshold decreases, goes through a minimum and…

We describe all the trees with the property that the corresponding edge ideal of the square of the tree has a linear resolution. As a consequence, we give a complete characterization of those trees $T$ for which the square is co-chordal,…

The article describes the structural and algorithmic relations between Cartesian trees and Lyndon Trees. This leads to a uniform presentation of the Lyndon table of a word corresponding to the Next Nearest Smaller table of a sequence of…

We consider a branching random walk on the lattice, where the branching rates are given by an i.i.d. Pareto random potential. We describe the process, including a detailed shape theorem, in terms of a system of growing lilypads. As an…

In a Lombardi drawing of a graph the vertices are drawn as points and the edges are drawn as circular arcs connecting their respective endpoints. Additionally, all vertices have perfect angular resolution, i.e., all angles incident to a…

In [3] L.Zapponi studied the arithmetic of plane bipartite trees with prime number of edges. He obtained a lower bound on the degree of tree's definition field. Here we obtain a similar lower bound in the following case. There exists a…

We revisit the so-called "Three Squares Lemma" by Crochemore and Rytter [Algorithmica 1995] and, using arguments based on Lyndon words, derive a more general variant which considers three overlapping squares which do not necessarily share a…

This paper is concerned with a shape optimization problem, where the functional to be maximized describes the total sunlight collected by a distribution of tree leaves, minus the cost for transporting water and nutrient from the base of the…

We define the branching ratio of the input tree of a node in a finite directed multigraph, prove that it exists for every node, and show that it is equal to the largest eigenvalue of the adjacency matrix of the induced subgraph determined…

The notion of friendliness between trees first appeared in solution of Lando's problem on intersection of polyhedra in 3-space. A tree is friendly to a path graph if edges of the tree can be numbered so that for each k,s the path between…

In SODA'99, Chan introduced a simple type of planar straight-line upward order-preserving drawings of binary trees, known as LR drawings: such a drawing is obtained by picking a root-to-leaf path, drawing the path as a straight line, and…

On folio 855 recto of the Codex Atlanticus, Leonardo da Vinci drew three 'easily movable' bridges, but one of them is enigmatic: all 'replicas' in Leonardo museums and exhibitions come as a surprise, to say the least, to any engineer or…

We consider the branching capacity of the range of a simple random walk on $\mathbb Z^d$, with $d \ge 5$, and show that it falls in the same universality class as the volume and the capacity of the range of simple random walks and branching…

We consider a sequence of sums of powers of the the roots of the cubic equation characterizing the Tribonacci sequences and derive its relationship with a particular Tribonacci sequence. Then we make a conjecture on the possible…

To each del Pezzo surface (resp. ruled surface, ruled surface with a section), we describe a natural Lie algebra bundle of type E_n (resp. D_n, A_n) over it. Using lines and rulings on any such surface, we describe various representation…

This study provides a general construction method of cell shape invariant by the Errera rule of division on a cone and provides analytical bounds for the apical angle of the cone on which these cells are connected and thus biologically…