Visualising Volumetric Fractals

Fractal images have for many years been a richsource of exploration by those in computer science who also havean interest in graphics. They often served as a way of testing theperformance of new computing hardware and to explore thecapabilities of emerging display technologies. While there havebeen forays by some into 3D geometric fractals, the 3Dequivalents of the Mandelbrot set have been largely ignored. Thisis largely due to the lack of suitable tools for rendering these setsexcept perhaps as isosurfaces, a rather unsatisfactory and limitedrepresentation. The following will illustrate the application ofGPU based raycasting, a now relatively standard approach tovolume rendering, to the representation of volumetric fractals.Leveraging existing software that has been designed for generalvolume visualisation allows the interested 3D fractal explorer tofocus on the mathematical generation of the volume data ratherthan reinventing the entire volume rendering pipeline

Automated Identification and Tracking of Deformation Twin Structures in Molecular Dynamics Simulations

Deformation twinning significantly influences the microstructure, texture, and mechanical properties of metals, necessitating comprehensive studies of twin formation and interactions. While experimental methods excel at analyzing individual samples, they often lack the capability for temporal analysis of twinned structures. Molecular dynamics simulations offer a temporal dimension, yet the absence of suitable tools for automated crystal twin identification has been a significant limitation. In this article, we introduce a novel computational tool integrated into the visualization and analysis software OVITO. Our tool automates the identification of coherent twin boundaries, links related twin boundaries, validates twin structures through orientation analysis, and tracks twins over time, providing quantifiable data and enabling in-depth investigations. Validation on a copper single crystal under shear loading demonstrates successful tracking of various twins, revealing their genesis and growth over multiple timesteps. This innovative approach promises to advance the computational materials science domain by facilitating the study of deformation twinning, offering profound insights into the behavior and mechanical performance of materials

Unlimited object instancing in real-time

In this paper, we propose a novel approach to efficient rendering of an unlimited number of 3D objects in real-time. We present a rendering pipeline that is based on a new computer graphics programming paradigm implementing a holistic approach to the virtual scene definition. Using Signed Distance Functions (SDF) for a virtual scene representation, we managed to control the content and complexity of the virtual scene with the use of mathematical equations. In order to solve the limited hardware problem, especially the limited capacity of the GPU memory, we propose a scene element repository which extends the idea of the data based amplification. The content of the repository strongly depends on a 3D object visualization method. One of the most important requirements of the developed pipeline is the possibility to render 3D objects created by artists. In order to achieve that, the object visualization method uses Sparse Voxel Octree (SVO) ray casting. The developed rendering pipeline is fully compatible with the available SVO algorithms. We show how to avoid occlusion errors which can occur in the SDF and SVO integration single-pass rendering pipeline. Finally, in order to control the content and complexity of the virtual scenes in an unlimited way, we propose a collection of global operators applicable to the virtual scene distance function. Developed Unlimited Object Instancing rendering pipeline can be easily integrated with traditional visualization methods, e.g. the triangle rasterization. The only hardware requirement for our approach is the support for compute shaders or any GPGPU API

Fractal Image Editing with PhotoFrac

In this paper, we describe the development and use of PhotoFrac, an application that allows artists and designers to turn digital images into fractal patterns interactively. Fractal equations are a rich source of procedural texture and detail, but controlling the patterns and incorporating traditional media has been difficult. Additionally, the iterative nature of fractal calculations makes implementation of interactive techniques on mobile devices and web apps challenging. We overcome these problems by using an image coordinate based orbit trapping technique that permits a user-selected image to be embedded into the fractal. Performance challenges are addressed by exploiting the processing power of graphic processing unit (GPU) and precomputing some intermediate results for use on mobile devices. This paper presents results and qualitative analyses of the tool by four artists (the authors) who used the PhotoFrac application to create new artworks from original digital images. The final results demonstrate a fusion of traditional media with algorithmic art

The AFLOW Fleet for Materials Discovery

The traditional paradigm for materials discovery has been recently expanded to incorporate substantial data driven research. With the intent to accelerate the development and the deployment of new technologies, the AFLOW Fleet for computational materials design automates high-throughput first principles calculations, and provides tools for data verification and dissemination for a broad community of users. AFLOW incorporates different computational modules to robustly determine thermodynamic stability, electronic band structures, vibrational dispersions, thermo-mechanical properties and more. The AFLOW data repository is publicly accessible online at aflow.org, with more than 1.7 million materials entries and a panoply of queryable computed properties. Tools to programmatically search and process the data, as well as to perform online machine learning predictions, are also available.Comment: 14 pages, 8 figure

Fractals with arbitrary segment lengths

Work in the area of fractal geometry has generally focused on a specific facet of the discipline at the expense of other interesting features. This approach often generates more questions than answers for the general audience due to the lack of unification across all views. It appears that a common thread to relate all aspects of fractal characteristics is missing. This paper addresses this question and presents some new and fascinating results. For example, in-depth mathematical analysis often defers to the intriguing and attractive graphical displays produced by mapping the complex plane to the pixel field on a CRT. Both area, mathematics and graphics, are generally developed or presented independently. the development of common attribute linkages is done separately or perhaps not at all. First, a completely modular survey of the state of the art concerning regular fractal geometry is given. In addition, a method for calculating the fractal dimension of asymmetric fractals is proposed, where a symmetric fractal is a special case of an asymmetric fractal --page iii

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