Related papers: Real-time rendering of complex fractals
A generalization of the filled-in Julia set is presented using the multicomplex numbers and an algorithm is presented to visualize these sets in the tridimensional space. There are many ways to visualize these higher dimensional fractals…
Optical images of transparent three-dimensional objects can be different from a replica of the object's cross section in the image plane due to refraction at the surface or in the body of the object. Simulations of the object's image are…
We discuss the challenges of modeling X-ray bursts in multi-dimensions, review the different calculations done to date, and discuss our new set of ongoing simulations. We also describe algorithmic improvements that may help in the future to…
In this short note, we merge the areas of hypercomplex algebras with that of fractal interpolation and approximation. The outcome is a new holistic methodology that allows the modelling of phenomena exhibiting a complex self-referential…
Creating realistic virtual assets is a time-consuming process: it usually involves an artist designing the object, then spending a lot of effort on tweaking its appearance. Intricate details and certain effects, such as subsurface…
We present a general theory of fractal transformations and show how it leads to a new type of method for filtering and transforming digital images. This work substantially generalizes earlier work on fractal tops. The approach involves…
Radiance Fields (RFs) have shown great potential to represent scenes from casually captured discrete views. Compositing parts or whole of multiple captured scenes could greatly interest several XR applications. Prior works can generate new…
We discuss the formation of stochastic fractals and multifractals using the kinetic equation of fragmentation approach. We also discuss the potential application of this sequential breaking and attempt to explain how nature creats fractals.
Large-scale numerical simulations of planetary interiors require dedicated visualization algorithms that are able to efficiently extract a large amount of information in an interactive and user-friendly way. Here we present a software…
The processes of radiation defects formation and evolution have been simulated in cubic dielectric crystals by the computational method of cellular automata. If suppose that the defects concentration as a parameter, which characterizes a…
We present a new object representation, called Dense RepPoints, that utilizes a large set of points to describe an object at multiple levels, including both box level and pixel level. Techniques are proposed to efficiently process these…
The observation of neutron interference by using a crystal interferometer having a separate analyser opens the way to the construction and operation of interferometers with vast arm separation and length. Setting the design specifications…
Many biological processes and objects can be described by fractals. The paper uses a new type of objects - blinking fractals - that are not covered by traditional theories considering dynamics of self-similarity processes. It is shown that…
We examine several currently used techniques for visualizing complex-valued functions applied to modular forms. We plot several examples and study the benefits and limitations of each technique. We then introduce a method of visualization…
This work proposes the development and study of a novel technique for the generation of fractal descriptors used in texture analysis. The novel descriptors are obtained from a multiscale transform applied to the Fourier technique of fractal…
We present a complete system for real-time rendering of scenes with complex appearance previously reserved for offline use. This is achieved with a combination of algorithmic and system level innovations. Our appearance model utilizes…
We describe a numerical model for the interaction of light with large raindrops using realistic nonspherical drop shapes. We apply geometrical optics and a Monte Carlo technique to perform ray traces through the drops. We solve the problem…
There are various notions of dimension in fractal geometry to characterise (random and non-random) subsets of $\mathbb R^d$. In this expository text, we discuss their analogues for infinite subsets of $\mathbb Z^d$ and, more generally, for…
We present the first real-time method for inserting a rigid virtual object into a neural radiance field, which produces realistic lighting and shadowing effects, as well as allows interactive manipulation of the object. By exploiting the…
In our previous work, On the localization of Hutchinson-Barnsley fractals, Chaos Solitons Fractals, 173 (2023), 113-674, we presented a method for finding a finite family of closed balls whose union contains the attractor of a given…