相关论文: Leonardo vindicated: Pythagorean trees for minimal…

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…

Fractal scaling--a power-law behavior of the number of boxes needed to tile a given network with respect to the lateral size of the box--is studied. We introduce a new box-covering algorithm that is a modified version of the original…

Fractals are geometric shapes that can display complex and self-similar patterns found in nature (e.g., clouds and plants). Recent works in visual recognition have leveraged this property to create random fractal images for model…

We introduce a framework for constructing fractal trees via analytic generator fields, replacing discrete affine transformations and symbolic rewriting rules by the integration of smooth vector fields in an internal state space. In this…

The issue of data-driven neural network model construction is one of the core problems in the domain of Artificial Intelligence. A standard approach assumes a fixed architecture with trainable weights. A conceptually more advanced…

Evolutionary Algorithms are naturally inspired approximation optimisation algorithms that usually interfere with science problems when common mathematical methods are unable to provide a good solution or finding the exact solution requires…

Fractal AI is a theory for general artificial intelligence. It allows deriving new mathematical tools that constitute the foundations for a new kind of stochastic calculus, by modelling information using cellular automaton-like structures…

The fractal dimension provides a statistical index of object complexity by studying how the pattern changes with the measuring scale. Although useful in several classification tasks, the fractal dimension is under-explored in deep learning…

Fractal geometry, defined by self-similar patterns across scales, is crucial for understanding natural structures. This work addresses the fractal inverse problem, which involves extracting fractal codes from images to explain these…

This paper proposes FractalNet, a framework based on fractal design principles that automatically generates and evaluates convolutional neural network (CNN) architectures using recursive template patterns. Rather than relying on…

By unifying three foundational principles of modern biology, we develop a mathematical framework to analyze the growing tree of life. Contrary to the static case, where the analogy between phylogenetic trees and the tree that grows in soil…

This study introduces a physics-based machine learning framework for modeling both brittle and ductile fractures. Unlike physics-informed neural networks, which solve partial differential equations by embedding physical laws as soft…

Dynamic trees are mixtures of tree structured belief networks. They solve some of the problems of fixed tree networks at the cost of making exact inference intractable. For this reason approximate methods such as sampling or mean field…

In this paper, we introduce a new concept: the transfinite fractal dimension of graph sequences motivated by the notion of fractality of complex networks proposed by Song et al. We show that the definition of fractality cannot be applied to…

We propose a novel stochastic network model, called Fractal Gaussian Network (FGN), that embodies well-defined and analytically tractable fractal structures. Such fractal structures have been empirically observed in diverse applications.…

A fractal is in essence a hierarchy with cascade structure, which can be described with a set of exponential functions. From these exponential functions, a set of power laws indicative of scaling can be derived. Hierarchy structure and…

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…

Analysis and modeling of networked objects are fundamental pieces of modern data mining. Most real-world networks, from biological to social ones, are known to have common structural properties. These properties allow us to model the growth…

If our aesthetic preferences are affected by fractal geometry of nature, scaling regularities would be expected to appear in all art forms, including music. While a variety of statistical tools have been proposed to analyze time series in…

This work presents a method for semantic segmentation of mango trees in high resolution aerial imagery, and, a novel method for individual crown detection of mango trees using segmentation output. Mango Tree Net, a fully convolutional…