Development Blog. | Xenofractals | Prof. Dr. G. Keith Still FIMA

Morphology - incrementing the orbital loop

Sun, 19 Feb 2012 17:34:34 +0000

In this series I'm incrementing the orbital loop - this results in wrapping the algorithm N times around a circle map.

Greens - just a change of palette

Sun, 19 Feb 2012 16:27:10 +0000

Amazing how a change in the palette generation algorithm can make such a difference to the appearance of these xenofractals.

Watching them grow

Sat, 18 Feb 2012 09:35:04 +0000

This short sequence (screen grabs) are from the new morphology program. These are all based mathematical interpretations inspired by D'Arcy Wentworth Thompson's "On Growth and Form" The complete revised edition (1992). This weekend I'm going to catalogue the morphology of these. The numbers on the top left refer to the function drivers.

Exploring more details

Sat, 18 Feb 2012 03:31:24 +0000

Another sleepless night - so coded a bit more on the new xenofractal explorer. This is a using different start points on a single function, letting it develop then starting again with a new start point to see how different the end result looks.

More variation on a theme

Fri, 17 Feb 2012 22:13:15 +0000

These are some experiments with palettes and the start and increment for the biological growth algorithms. I've also a range of Galaxy algorithms (using the gravitational equations as a basis for long term stability). The origin of these algorithms comes from a symplectic integration equation from the New Scientist back in 1994 (ish). However since then I've been experimenting with equations from interactive growth (e.g.: using a growth function upon the computer screen similar to a "petri" dish and mould growth.

These are all variations on a theme from one set of equations and different palettes to display the details.

Variation on a theme

Fri, 17 Feb 2012 04:48:19 +0000

I wanted to see more detail on the centre of this xenofractal image - so zooming in ….

I got this - then increasing the resolution (to do this I reduce the incremental step size in the generation algorithm - creating more intermediary points. Also changed the screen size from 1024 x 768 to 1100 x 800

At the time I was using Team viewer with Alex (we are working on network analysis algorithms). He liked this one a lot - so now this is "Alex's Xenofractal". This weekend we're going to upgrade the iPad programme to include deep zoom on these images. Should be out in a week or so (depending on Apple approval process).

Incredible detail on these new algorithms

Thu, 16 Feb 2012 02:00:14 +0000

Couldn't sleep - so been experimenting with some complex functions on the Xenofractal Generator. Although this is only using a limited "fire" palette the images are hypnotic when growing and have some incredible detail. Now to recode this for the iPad as they are stunning to watch develop on the screen.

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New Hi-resolution images

Wed, 15 Feb 2012 09:49:29 +0000

Now plotting 1024 x 768 32 bit image. Image 21 (below) uses just the red palette. Great to see the old xenofractals in hi-resolution. Far more spectacular than the 640x480 16 colour versions. Now working on multiple function code and importing all the old algorithms.

Increased Resolution and Colour Depth

Sat, 11 Feb 2012 09:24:19 +0000

32 bit resolution colours, increased the size of the screen to 1024, 768 - these are amazing to watch grow - will be creating hi-res movies of these over the next week.

New Xenofractals - QB64 code

Thu, 09 Feb 2012 03:07:54 +0000

Sleepless nights and coding are always great fun.

I've been experimenting with the original experimental code and loading into Mac Qb64 to produce a few of the "organic" type patterns. Cataloguing under their original "raw code" titles before I define the genotypes for this family of functions.

Xenofractal 47

Xenofractal 30

Xenofractal 30a

Xenofractal 31

Xenofractal 32

New Geometry - extract from "The Shadow of the Cobweb."

Sun, 05 Feb 2012 07:37:18 +0000

A new geometry...

March 1994 brought an article in New Scientist magazine about something called symplectic geometry, one ingredient of chaos theory. 'Symplectic' just means 'complex', but its mathematical associations are those of the complex numbers, in which minus one has a square root. In symplectic space a line is always at right angles to itself. Symplectic geometry includes velocities as well as positions, it is a geometry of motion. Well, he needed a new geometry, and since this one was on offer... He entered some sample formulas into his computer, trying to use symplectic geometry to model the motion of individuals in crowds. Suddenly, on the screen, in vivid colour, growing before his eyes, were the most striking, mysterious, and downright beautiful images that he'd ever seen. There were hundreds of them, thousands, millions. Every new 'seed' number that he fed his computer produced a new and different image.

For the full story by Ian Stewart - click here.

New QB64 code

Sat, 04 Feb 2012 14:24:58 +0000

Installed QB64 for the Mac today - cataloguing the older xenofractals - using the screen grab and producing some stunning images. Although this is taking a bit of time to convert the QB45 to text then to rename, then import, make some minor modifications, then using a manual screen grab I can at least access all my old work. Including the market/trading models (based on integrate and fire cellular automata). Below is the image from the Mac. Lots more to come and the morphology (work I did for my PhD but never published).

New Mac Program

Wed, 01 Feb 2012 22:06:08 +0000

A couple of images from the new Mac (Xcode) project. Much higher resolution and the new iPad program was launched on Sunday night.

Click on the logo get the free iPad app from iTunes.

Screen shots from the iPad program

Sat, 28 Jan 2012 10:20:38 +0000

This is a screen shot from the iPad program - launched in October and waiting for Apple to verify the new upload (with explore and save options, higher resolution, screen orientation lock and much more.

Weekend working

Sat, 28 Jan 2012 09:19:43 +0000

New code for the Mac. Seem to have a different orientation to the older QB45 programme - X and Y coordinates. Working on making this produce video clips, new palette options and sorting out the massive back catalogue. Now that I've saved all the old parameters in text form and converted everything into a more readable format - all that is left to do is find a suitable framework for the Mac.

Xcode seems to be great - but very alien (thinks - it was over 18 years since I was last coding and back then it was all self taught). So choosing the right programming environment and parsing all the old code will be a lot of work - but this is great fun.

Fragment below of the new screen resolution on the Mac….

New Website and Old Code

Sun, 22 Jan 2012 21:48:54 +0000

New website created and links to a variety of fractal and mathematical forums.

I've over 20 years of notebooks and experimental code (all in a folder which now has 334 "raw" code segments and two explorer programmes I wrote in Quick Basic….trying to figure out how to convert these into plain text so I can read them. I may have to use a very old computer to do that since I'm not sure QB45 will run under Windows 7…..lots of hobby work ahead I think…..

Xenofractals and the iPad App.

Sun, 22 Jan 2012 20:27:14 +0000

Well it's been nearly 20 years since I first began to catalogue these strange attractors - not really been able to explore them to any extend for the last 15 years but the time has come to do something interesting and artistic. The XenoFractals* were derived from an article in New Scientist about symplectic integrators and so far they have three distinct properties:

The first is they product very interesting, biological shapes (see image gallery).

I've catalogued many hundreds of these and they look very similar to Diatoms. Each Xenofractal has deep zoom details - my programming skills were never that great - so a friend (Alex Ryzhanskiy) has coded the iPad application (just sent version 2 to Apple for review).

Click on the logo get the free iPad app from iTunes.

I've a heap of old code to sift through (Quick Basic) and hopefully we will have a Window 7, Mac and iPad version running in the next few weeks.

Left and right diatoms. These are microscopic particles that form colonies. Below are a series of xenofractals showing the similarity to diatomic patterns.