# Generative Art, 3D Fractals, Creative Computing

Related:  2018 Décembre2021 Novembre

Polytopes and Coxeter Groups My first encounter with four-dimensional polytopes was Jenn 3D (2001-2007) by Fritz Obermeyer. Jenn describes itself as follows: Jenn is a toy for playing with various quotients of Cayley graphs of finite Coxeter groups on four generators. Jenn builds the graphs using the Todd-Coxeter algorithm, embeds them into the 3-sphere, and stereographically projects them onto Euclidean 3-space. Wow. We will also go one step further, and discuss how these structures can be ray traced in realtime. Symmetries of the cube We will start out in three dimensions with a familiar object: the cube. The cube has several automorphisms - transformations that will map the cube onto itself. Including the identity transformation, and taking into account that we could also mirror each one of these transformations, we arrive at 48 automorphisms for the cube. Besides the rotation symmetries above, we can also depict the reflection symmetries. This means we can establish the following relations between the generators:

Fragmentarium In some ways path tracing is one of the simplest and most intuitive ways to do ray tracing. Imagine you want to simulate how the photons from one or more light sources bounce around a scene before reaching a camera. Each time a photon hits a surface, we choose a new randomly reflected direction and continue, adjusting the intensity according to how likely the chosen reflection is. Though this approach works, only a very tiny fraction of paths would terminate at the camera. So instead, we might start from the camera and trace the ray from here and until we hit a light source. And, if the light source is large and slowly varying (for instance when using Image Based Lighting), this may provide good results. But if the light source is small, e.g. like the sun, we have the same problem: the chance that we hit a light source using a path of random reflections is very low, and our image will be very noisy and slowly converging. Diffuse reflections How to solve the rendering equation and Sky model

Distance Estimated 3D Fractals (III): Folding Space The previous posts (part I, part II) introduced the basics of rendering DE (Distance Estimated) systems, but left out one important question: how do we create the distance estimator function? Drawing spheres Remember that a distance estimator is nothing more than a function, that for all points in space returns a length smaller than (or equal to) the distance to the closest object. It is fairly easy to come up with distance estimators for most simple geometric shapes. (1) DE(p) = max(0.0, length(p)-R) // solid sphere, zero interior (2) DE(p) = length(p)-R // solid sphere, negative interior (3) DE(p) = abs(length(p)-R) // hollow sphere shell From the outside all of these look similar. What about the first two? From left to right: Sphere (1), with normal artifacts because the normal was not backstepped. Notice that distance estimation only tells the distance from a point to an object. Combining objects Distance fields have some nice properties. So now we have a way to combine objects.

Fixed Gear Calculator - Ratio & Skid Patch for all! Le "Fantastic Fixed Gear Calculator" vous est gentillement offert par l'quide de SURPLACE, ouai ouai on est sympa. Toutes les donnes relatives aux circonfrences de pneu proviennent du fantastique site de Sheldon Brown. Merci lajalousie pour les corrections apportes au calcul des skid patchs ambidextres A cause du manque de support (correct) des canvas et d'html5, a ne marchera probablement pas (ou mal) dans Internet Explorer, mais a intresse qui? Alors profitez !

Generative Art Links Some links to Generative Art, Math & Fractals, and other creative ways of creating computional imagery. The list is not meant to be exhaustive: rather, it is a list of my favorite links. Generative Art Software General-Purpose Software Processing is probably the most used platform for Generative Art. Nodebox – A Python based alternative to Processing. vvvv is “a toolkit for real time video synthesis”. PureData a “real-time graphical dataflow programming environment for audio, video, and graphical processing.” Specific Systems Context Free Art – uses Context Free Design Grammars to generate 2D images. Structure Synth – my own attempt to extend Context Free Art into three dimensions. TopMod3D – “is a free, open source, portable, platform independent topological mesh modeling system that allows users to create high genus 2-manifold meshes”. Ready. K3DSurf – 3D surface generator (for a nice example check out this one by Schmiegl). Fractals and Math Art Software Fragmentarium. GLSL Sandbox by Mr.

Architecture pour la Liturgie – Aménagement des espaces sacrés au service de la Liturgie catholique Bonus: Luma Pictures’ new tools for Doctor Strange Doctor Strange has been a huge film for Marvel. To achieve their sections of the film, Luma Pictures developed a set of new tools, including some they will even be sharing with the community. Luma Pictures worked on several key sequences including the opening London sequence and they also booked ended the film with the Dormammu sequence and the Dark realm. London For the London sequence Luma developed a new fractal tool to do volumetric meshing and transforming of the buildings. "With what we needed to do we needed to art direct the speed, the movement and look at all of these 'fractals'," says Cirelli. Luma pictures literally choreographed the fractals, "which is not an easy task." The Mandelboxes are different from Mandleblubs used the film Suicide Squad. "The Mandelbox that we used allowed us to do all the arranging, mirroring and manipulation of the frequency of the volume of the London buildings, along with all the slicing and dicing," explained Cirelli. Vince Cirelli VFX Supervisor