mathr / blog / #

Affine-conjugation to move the critical point to 0 to avoid precision loss.

In which various initial guesses for Newton's method are tested.

Many new features, bugfixes and speed improvements.

A fractal music video with both zooming and non-zooming parts.

Analysis of a fractal artwork by JWM.

Co.Lab Sounds is back again with Fringe Art Bath for their 2021 festival!

Many enhancements for speed and comfort.

Embedding a 2D image into a 1D palette that gets wrapped back to 2D by fractal spirals.

Perturbation and rescaling for efficient rendering of fractal images.

Synchronizing fractal zooms to audio with kf-2.15.2 and zoomasm-3.0.

Supporting custom colouring algorithms direct from KF 2.15.2.

Design your own custom colouring algorithms in OpenGL GLSL shader fragments.

Optimal in the sense of most uniform distribution of points.

Plenty more bug fixes, plus a new feature. Also belated 2.0 release announcement.

Plenty of bug fixes, plus GUI transparency controls and PPM export without FFmpeg.

OpenCL acceleration, hybrid formula designer, exponential map, and more.

First release of the zoom video assembler.

Finding the optimal zoom ratio when reusing the center portion.

Co.Lab Sound experimental test bed for collaborative live and sound art at Fringe Arts Bath online festival.

Lots of new features, lots of bug fixes, lots of speed improvements.

Histograms of histograms to blur separably bucket by bucket.

Not a Mandelbrot set deep zoom, but it might resemble one at first glance with its nested period-doubling crises.

Pull back a path from iterates of \(\theta\) to find \(c_{\theta}\).

Gluing two \(z^2+c\) quadratic Julia sets sometimes gives a \(\frac{z^2+a}{z^2+b}\) rational Julia set.

Two ways of rendering the 4D Mandelbrot/Julia/Buddhabrot hologram.

An extra branch is floated out. Plus SIMD to make it even faster.

Conference paper: At the Helm of the Burning Ship

Photos of exhibition at Chalton Gallery, by Pau Ros.

Digital art, computer graphics, Free/Libre open source software. 12-27th April 2019.

A multiple copy reduction machine via linked images.

Reject lower periods, and iteratively perturb a known cycle along a path.

A small region bouncing around the dynamical plane seldom touches an axis.

Based on the size estimate for mini-ships, use derivative matrices to calculate optimal viewing transformation.

An implementation of someone else's paper.

How to determine the number of Misiurewicz points of a given (pre)period in the Mandelbrot Set.

My a/v work Puzzle is part of a group show, 6th-22nd August 2018.

Exploring the fertility of errors and questioning our inherited worldview.

A collection of rules for deriving perturbed iterations.

Regions surrounding mini-ships.

A fractal like the Mandelbrot set but with absolute values thrown in to the mix.

Model the whole complex plane via the Riemann sphere as an OpenGL cube map.

Keyframe animation and the return of single precision support with OpenGL 3.3 (OpenGL 4 double precision still an option)

Nucleus finding, Misiurewicz point finding, and a bit of guesswork, combine for successful O(period) automatic Julia morphing.

Improving image quality by avoiding catastrophic cancellations.

Worst-case guess improved by a factor of 8.

Highlighting previously invisible periodic properties in the Mandelbrot set.

Finding periodic points in the Mandelbrot set to make annotated images.

Using third-party libraries for acceleration.

Double precision using OpenGL 4 to avoid postpone ugly artifacts.

Inflection mapping for complex quadratic polynomials.

January 12th to February 5th, Centro Conde Duque, Madrid, Spain.

How they did it, as far as I can tell.

Black-and-white flame fractals synchronized with rich ambient drones.

Experimental OpenGL driver used by Pd and Gem with PdLua seems to work mostly fine.

A familiar picture emerges.

Notes on a conjecture of Aaron Klebanoff.

Tracing the boundaries of hyperbolic components.

Piecewise integer recurrence translated to complex function.

Additive blending reveals many things.

Infinite fractal television zoom

Sliced rendering, improved glitch correction, reduced video memory usage, and more.

Big bad bugs been debugged, and nifty features added.

Lots of changes in a short space of time.

Sometimes simple approaches are better.

Automatic glitch correction, zoom sequence rendering, tiled rendering for high resolution or anti-aliasing, ...

Trace a number of probe points in the atom domain.

Combining saved flake images using command line tools.

From many raw 2fold zoom images to one long strip.

A modified bump-mapping approach.

Subdivide only near the boundary.

Around embedded Julia sets in the Mandelbrot set.

Using Newton's method.

Fixing code from 1992.

Rebasing from a reference point.

Handwritten notes on various properties.

An xmas present for someone special.

Conformal mapping using Möbius transformations.

Rewritten in portable C.

A series of approximations result in a simple formula.

Exploring external angles.

Derived from continuous escape time.

Structures in the hairs.

Derived from distance estimation for Julia sets.

Some notes on various aspects of design and potential implementation.

another representation function

cutting and pasting binary digits of external angles

finding tuned branch points

speeding up external ray tracing

Mandelbrot Set explorer using OpenGL 4

New website, new beginnings.

26 images of the Mandelbrot Set

Following distance estimates.

Lots to think about.

Now hopefully more easily installable.

No algorithm to check open set condition.