fractal
Deep zoom theory and practice (again)
Perturbation with rebasing, and bilinear approximation, for efficient rendering of fractal images.
Perturbing Nova
Affine-conjugation to move the critical point to 0 to avoid precision loss.
External ray tracing
In which various initial guesses for Newton's method are tested.
Julia morph orbit in the hairs
A fractal music video with both zooming and non-zooming parts.
FaB Co.Lab 2021
Co.Lab Sounds is back again with Fringe Art Bath for their 2021 festival!
Legendary Colour Palette
Embedding a 2D image into a 1D palette that gets wrapped back to 2D by fractal spirals.
Deep zoom theory and practice
Perturbation and rescaling for efficient rendering of fractal images.
Wurgo music video and Making Of
Synchronizing fractal zooms to audio with kf-2.15.2 and zoomasm-3.0.
zoomasm 3.0 released
Supporting custom colouring algorithms direct from KF 2.15.2.
kf 2.15.2 released
Design your own custom colouring algorithms in OpenGL GLSL shader fragments.
Optimizing weights for iterated function systems
Optimal in the sense of most uniform distribution of points.
zoomasm 2.1 released
Plenty more bug fixes, plus a new feature. Also belated 2.0 release announcement.
zoomasm 1.1 released
Plenty of bug fixes, plus GUI transparency controls and PPM export without FFmpeg.
kf 2.15 released
OpenCL acceleration, hybrid formula designer, exponential map, and more.
Optimizing zoom animations again
Finding the optimal zoom ratio when reusing the center portion.
FaB Co.Lab
Co.Lab Sound experimental test bed for collaborative live and sound art at Fringe Arts Bath online festival.
KF 2.14.10 released
Lots of new features, lots of bug fixes, lots of speed improvements.
Fast density estimation
Histograms of histograms to blur separably bucket by bucket.
Crisis (deep zoom)
Not a Mandelbrot set deep zoom, but it might resemble one at first glance with its nested period-doubling crises.
Spider algorithm with a path
Pull back a path from iterates of \(\theta\) to find \(c_{\theta}\).
Slow mating of quadratic Julia sets
Gluing two \(z^2+c\) quadratic Julia sets sometimes gives a \(\frac{z^2+a}{z^2+b}\) rational Julia set.
Ultimate Anti-Buddhagram
Two ways of rendering the 4D Mandelbrot/Julia/Buddhabrot hologram.
Making KF fast again
An extra branch is floated out. Plus SIMD to make it even faster.
Exhibition (Chalton Gallery, London)
Digital art, computer graphics, Free/Libre open source software. 12-27th April 2019.
IFS fractals in Inkscape
A multiple copy reduction machine via linked images.
Newton's method for periodic cycles
Reject lower periods, and iteratively perturb a known cycle along a path.
Series approximation for the Burning Ship
A small region bouncing around the dynamical plane seldom touches an axis.
Unskewing the Burning Ship
Based on the size estimate for mini-ships, use derivative matrices to calculate optimal viewing transformation.
Enumeration of Misiurewicz points
How to determine the number of Misiurewicz points of a given (pre)period in the Mandelbrot Set.
Sounding DIY (Split)
My a/v work Puzzle is part of a group show, 6th-22nd August 2018.
eRR0R(iii)
Exploring the fertility of errors and questioning our inherited worldview.
Perturbation algebra
A collection of rules for deriving perturbed iterations.
The Burning Ship
A fractal like the Mandelbrot set but with absolute values thrown in to the mix.
Iterated function systems with cube maps
Model the whole complex plane via the Riemann sphere as an OpenGL cube map.
Inflector Gadget v0.3.2
Keyframe animation and the return of single precision support with OpenGL 3.3 (OpenGL 4 double precision still an option)
Efficent automated Julia morphing
Nucleus finding, Misiurewicz point finding, and a bit of guesswork, combine for successful O(period) automatic Julia morphing.
A more accurate elliptic variation
Improving image quality by avoiding catastrophic cancellations.
On the precision required for size estimates
Worst-case guess improved by a factor of 8.
Filtered atom domains
Highlighting previously invisible periodic properties in the Mandelbrot set.
Periodicity scan
Finding periodic points in the Mandelbrot set to make annotated images.
Inflector Gadget v0.2
Double precision using OpenGL 4 to avoid postpone ugly artifacts.
Monotone at MADATAC 08
January 12th to February 5th, Centro Conde Duque, Madrid, Spain.
Monotone at Mozilla Festival
Black-and-white flame fractals synchronized with rich ambient drones.
Puzzle on Raspberry Pi
Experimental OpenGL driver used by Pd and Gem with PdLua seems to work mostly fine.
Collatz fractal
Piecewise integer recurrence translated to complex function.
Lyapunov atom domains for negative multibrot sets
Additive blending reveals many things.
mightymandel v16
Sliced rendering, improved glitch correction, reduced video memory usage, and more.
mightymandel v12 - now twice as fast!
Sometimes simple approaches are better.
mightymandel updates galore
Automatic glitch correction, zoom sequence rendering, tiled rendering for high resolution or anti-aliasing, ...
Automatically finding external angles
Trace a number of probe points in the atom domain.
Making seasonal cards with Snowglobe
Combining saved flake images using command line tools.
Exponential mapping with Kalles Fraktaler
From many raw 2fold zoom images to one long strip.
Adaptive super-sampling using distance estimate
Subdivide only near the boundary.
Atom domain size estimation
A series of approximations result in a simple formula.
Distance estimation for Newton fractals
Derived from distance estimation for Julia sets.
A roadmap for distributed Mandelbrot set rendering
Some notes on various aspects of design and potential implementation.