3D Mandelbulb Ray Tracer. Published on 13 December 2009 The search for a true 3D Mandelbrot has been sought unsuccessfully for a number of years.
However, recently Daniel White, Paul Nylander and many others on FractalForums found that a slightly different approach yielded a true fractal structure in three dimensions; that is the images continue to reveal finer details the closer you look. If you want to dive right in and give it a go then jump to the project page. How it works The fractal calculation follows a similar process as a normal Mandelbrot set using the same formula,w' = wn + c, but instead of using standard complex numbers w and c are hyper-complex 'triplex' numbers with three components corresponding to the Cartesian x, y, and z co-ordinates. The triplex number w is raised to a power n using the following terms: w = {x, y, z}n = rn { sin(θn) cos(φn), sin(θn) sin(φn), cos(θn) } where:r = sqrt( x2 + y2 + z2 )θ = atan2( sqrt( x2 + y2 ), z )φ = atan2( y, x ) distance estimation = 0.5 * |w| * log(|w|) / |δw| 3D Mandelbulb Fractal Ray Tracer.
This implementation was written as a Pixel Bender filter then ported over to QuartzComposer as a GLSL patch to enable animation.
The scripts run on the GPU which makes real-time interactive exploration possible. For more information behind the discovery of the Mandelbulb see the accompanying blog post. More images in the gallery and on Flickr. Animation Animations can be created in Adobe After Effects using the .pbk files, but it will be very slow to render as the calculations have to be performed on the CPU rather than the GPU. Download and installation Download the 3D Mandelbulb Ray Tracer Note: there are two versions of each filter, the quick and and the normal. For Pixel Bender open the Mandelbulb.pbk file with the Adobe Pixel Bender Toolkit or copy it into the Pixel Bender Files folder in your Photoshop CS4 installation directory (you will need to have installed the PB plugin for Photoshop first). How to use Defining the fractal power: the power n used in the fractal equation. Navigation. Working with Quartz Composer.
Sprite Kit Sprite Kit is a powerful graphics framework for 2D games such as side-scrolling shooters, puzzle games, and platformers.
A flexible API lets developers control sprite attributes such as position, size, rotation, gravity, and mass. Sprite Kit’s OpenGL-based renderer efficiently animates 2D scenes. Built-in support for physics makes animations look real, and particle systems create essential game effects such as fire, explosions, and smoke. To assist SpriteKit-based game development, Xcode supports texture atlas creation and includes a particle creator. Scene Kit Scene Kit is a high-level Objective-C framework that enables your app to efficiently load, manipulate and render 3D scenes. Core Animation Core Animation lets you build dynamic, animated user experiences using an easy programming model based on compositing independent layers of media. Core Image Core Image is, simply put, “image effects made easy.”
Quartz OpenGL. How To Install Quartz Composer. These instructions are out-of-date!
Check out iLoveQC for a better reference on How To Install Quartz Composer Quartz Composer is an awesome realtime graphics tool, and comes free with OS X 10.4 and up. To install, run the XCode Tools installer from your System Install Disc. If you’re not going to be developing applications, then you can do a custom install of just the ‘Developer Tools Software’ package, which requires the BSD Package and the Mac OS X SDK Package (all on your Disc). Once installed, you can find it in HD > Developer > Applications > Graphics Tools > Quartz Composer. My First-Run Recommendations: Hit ‘Cancel’ on the New Composition from Template screen, go to Preferences, and choose At application startup: Do nothing. Now you’re ready to get started.