Related papers: Fractal structures in Adversarial Prediction
We introduce a design strategy for neural network macro-architecture based on self-similarity. Repeated application of a simple expansion rule generates deep networks whose structural layouts are precisely truncated fractals. These networks…
We show that when the standard techniques for calculating fractal dimensions in empirical data (such as the box counting) are applied on uniformly random structures, apparent fractal behavior is observed in a range between physically…
The adversarial attack literature contains a myriad of algorithms for crafting perturbations which yield pathological behavior in neural networks. In many cases, multiple algorithms target the same tasks and even enforce the same…
The term fractal describes a class of complex structures exhibiting self-similarity across different scales. Fractal patterns can be created by using various techniques such as finite subdivision rules and iterated function systems. In this…
We forge connections between the theory of fractal sets obtained as attractors of iterated function systems and process calculi. To this end, we reinterpret Milner's expressions for processes as contraction operators on a complete metric…
According to the fundamental principle of evolutionary game theory, the more successful strategy in a population should spread. Hence, during a strategy imitation process a player compares its payoff value to the payoff value held by a…
For a spatial characteristic, there exist commonly fat-tail frequency distributions of fragment-size and -mass of glass, areas enclosed by city roads, and pore size/volume in random packings. In order to give a new analytical approach for…
The aim of this paper is to analyse the Bitcoin in order to shed some light on its nature and behaviour. We select 9 cryptocurrencies that account for almost 75\% of total market capitalisation and compare their evolution with that of a…
We have developed a simulation technique that uses non-linear finite element analysis and elastic fracture mechanics to compute physically plausible motion for three-dimensional, solid objects as they break, crack, or tear. When these…
Observations of galaxies over large distances reveal the possibility of a fractal distribution of their positions. The source of fractal behavior is the lack of a length scale in the two body gravitational interaction. However, even with…
When trying to solve a computational problem, we are often faced with a choice between algorithms that are guaranteed to return the right answer but differ in their runtime distributions (e.g., SAT solvers, sorting algorithms). This paper…
The theory of resource distribution in self-organizing systems on the basis of the fractal-cluster method has been presented. In turn, the fractal-cluster method is based on the fractal-cluster relations of V.P. Burdakov and the analytical…
We study the kinetics of random sequential adsorption of a mixture of particles with continuous distribution of sizes for different deposition rules. It appears in the long time limit the resulting system can be described using the fractal…
We develop a new definition of fractals which can be considered as an abstraction of the fractals determined through self-similarity. The definition is formulated through imposing conditions which are governed the relation between the…
This preliminary paper presents initial explorations in rendering Iterated Function System (IFS) fractals using a differentiable rendering pipeline. Differentiable rendering is a recent innovation at the intersection of computer graphics…
We establish a correspondence between Pavlovian conditioning processes and fractals. The association strength at a training trial corresponds to a point in a disconnected set at a given iteration level. In this way, one can represent a…
Fractal surfaces ('patchwork quilts') are shown to arise under most general circumstances involving simple bitwise operations between real numbers. A theory is presented for all deterministic bitwise operations on a finite alphabet. It is…
Graphical models can represent a multivariate distribution in a convenient and accessible form as a graph. Causal models can be viewed as a special class of graphical models that not only represent the distribution of the observed system…
One of the most well known random fractals is the so-called Fractal percolation set. This is defined as follows: we divide the unique cube in $\mathbb{R}^d$ into $M^d$ congruent sub-cubes. For each of these cubes a certain retention…
The concept of self-similarity on subsets of algebraic varieties is defined by considering algebraic endomorphisms of the variety as `similarity' maps. Self-similar fractals are subsets of algebraic varieties which can be written as a…