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Register a new userEvolution of natural patterns from random fields
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In the article a transition from pattern evolution equation of reaction-diffusion type to a cellular automaton (CA) is described. The applicability of CA is demonstrated by generating patterns of complex irregular structure on a hexagonal and quadratic lattice. With this aim a random initial field is transformed by a sequence of CA actions into a new pattern. On the hexagonal lattice this pattern resembles a lizard skin. The properties of CA are specified by the most simple majority rule that adapts selected cell state to the most frequent state of cells in its surrounding. The method could be of interest for manufacturing of textiles as well as for modeling of patterns on skin of various animals.
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Mimicking natural tessellation patterns is a fascinating multi-disciplinary problem. Geometric methods aiming at reproducing such partitions on surface meshes are commonly based on the Voronoi model and its variants, and are often faced with challenging issues such as metric estimation, geometric, topological complications, and most critically parallelization. In this paper, we introduce an alternate model which may be of value for resolving these issues. We drop the assumption that regions need to be separated by lines. Instead, we regard region boundaries as narrow bands and we model the partition as a set of smooth functions layered over the surface. Given an initial set of seeds or regions, the partition emerges as the solution of a time dependent set of partial differential equations describing concurrently evolving fronts on the surface. Our solution does not require geodesic estimation, elaborate numerical solvers, or complicated bookkeeping data structures. The cost per time-iteration is dominated by the multiplication and addition of two sparse matrices. Extension of our approach in a Lloyds algorithm fashion can be easily achieved and the extraction of the dual mesh can be conveniently preformed in parallel through matrix algebra. As our approach relies mainly on basic linear algebra kernels, it lends itself to efficient implementation on modern graphics hardware.
We present a method of generating high resolution 3D shapes from natural language descriptions. To achieve this goal, we propose two steps that generating low resolution shapes which roughly reflect texts and generating high resolution shapes which reflect the detail of texts. In a previous paper, the authors have shown a method of generating low resolution shapes. We improve it to generate 3D shapes more faithful to natural language and test the effectiveness of the method. To generate high resolution 3D shapes, we use the framework of Conditional Wasserstein GAN. We propose two roles of Critic separately, which calculate the Wasserstein distance between two probability distribution, so that we achieve generating high quality shapes or acceleration of learning speed of model. To evaluate our approach, we performed quantitive evaluation with several numerical metrics for Critic models. Our method is first to realize the generation of high quality model by propagating text embedding information to high resolution task when generating 3D model.
Shortcuts in a regular architecture affect the information transport through the system due to the severe decrease in average path length. A fundamental new perspective in terms of pattern formation is the destabilizing effect of topological perturbations by processing distant uncorrelated information, similarly to stochastic noise. We study the functional coincidence of rewiring and noisy communication on patterns of binary cellular automata.
Sample patterns have many uses in Computer Graphics, ranging from procedural object placement over Monte Carlo image synthesis to non-photorealistic depiction. Their properties such as discrepancy, spectra, anisotropy, or progressiveness have been analyzed extensively. However, designing methods to produce sampling patterns with certain properties can require substantial hand-crafting effort, both in coding, mathematical derivation and compute time. In particular, there is no systematic way to derive the best sampling algorithm for a specific end-task. Tackling this issue, we suggest another level of abstraction: a toolkit to end-to-end optimize over all sampling methods to find the one producing user-prescribed properties such as discrepancy or a spectrum that best fit the end-task. A user simply implements the forward losses and the sampling method is found automatically -- without coding or mathematical derivation -- by making use of back-propagation abilities of modern deep learning frameworks. While this optimization takes long, at deployment time the sampling method is quick to execute as iterated unstructured non-linear filtering using radial basis functions (RBFs) to represent high-dimensional kernels. Several important previous methods are special cases of this approach, which we compare to previous work and demonstrate its usefulness in several typical Computer Graphics applications. Finally, we propose sampling patterns with properties not shown before, such as high-dimensional blue noise with projective properties.
We present the pattern underlying some of the properties of natural numbers, using the framework of complex networks. The network used is a divisibility network in which each node has a fixed identity as one of the natural numbers and the connections among the nodes are made based on the divisibility pattern among the numbers. We derive analytical expressions for the centrality measures of this network in terms of the floor function and the divisor functions. We validate these measures with the help of standard methods which make use of the adjacency matrix of the network. Thus how the measures of the network relate to patterns in the behaviour of primes and composite numbers becomes apparent from our study.
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