Submitted by Torsten Stier on
From the technical side most of the clips are simple Mandelbox fractals, some of them with a negative scale and rotated folding planes. The fractal clips were completely rendered in Mandelbulber 1.21 OpenCL and CPU mode
Submitted by Torsten Stier on
Exhibition of 31 big prints by Torsten Stier and some of his animations.
There will be a Vernissage on October 2nd with a short lecture about the history of fractals and fractal art.
During the week a workshop about the basics of 3d fractal generation will take place and the results of this workshop will be displayed at the Finissage on October 9th.
Info and registration: Majda Gutlić
Submitted by Torsten Stier on
Torsten Stier has been one of the pioneers in the artistic use of 3d fractals since 2010. His award winning movies combine the current peak of fractal animation rendering with precise editing. The results are stunning multi-media pieces, that carry the concept of music videos to a different stage.
Besides the films Torsten also shows several hi-res, large format prints with up to 68 Megapixels, that display the rich details of his fractals far beyond screen resolution.
Further more there will be a presentation with a brief history of fractals from the early math monsters of the 19th century to the latest developments in 3d fractal generation.
The sound support of this evening will be given by the world famous trance DJ Taucher. Taucher’s sound sculptures will provide the ambience for the social part of the evening…
doors 6pm
beginning 8pm
Submitted by Torsten Stier on
The approach
Fundamental transformation of the Mandelbrottian iteration (z=z²+c) is the squaring of a complex number represented in z². In the vectorial view this corresponds to a rotational extension of the position vector of a point. In other words, this is a circular transformation with subsequent scaling. In the Mandelbox, a spherical transformation is performed (the so-called BallFold) with subsequent scaling. This is already the whole trick. There is further a BoxFold for the shape and – as with Mandelbrot – the addition of a constant c.
Please consider that this reflects a most simplified and pointed geometric view. The algebraic view is more complex and needs a high level of abstraction, but gives us the opportunity to calculate and study this object. In the end formulas (see bottom left) and algorithms, does not tell us much about the shape created with a certain parameter set and unforunately humans have no real sense for that kind of math. So we need to try out. And here the geometric view is pretty useful.
Algorithmic descriptions and other background you find in Tom Lowe’s initial publication
https://sites. google.com/site/mandelbox/what-is-a-mandelbox
My image sea invader is part of IMAGINARY: Beauty and power of mathematics
https://www. imaginary.org/gallery/exhibition-beauty-and-power-of-mathema…
with an excellent formal implementation by Prof. Paul Igodt
In most common 3d fractal software – Mandelbulber and Mandelbulb3d – the default starting Parameter at a scale of two
A purely bold display of the relationship between the Mandelbox and the Mandelbrot set. A formal mathematical connection cannot be derived from this.
An image of 2011, from the early days of the Mandelbox. The Mandelbox can also be scaled negatively, which corresponds to a rotation of 180°. With additional rotations of about 0°±15°, images like this one are created. One of the first parameters, I converted to Mandelbulb3d. With help of Jens Dierks (aka Jesse) - the Programmer of M3d.
In fact Jesse wrote a little tool, that converts rotation angles between the programmes. Rotations are not commutative in three dimensions (means x+y+z ≠ z+y+x) and m3d rotates x-axis first and Mandelbulber the z-axis.
This tool can still be found at the old fractal forums
Image published in: Benoit Mandelbrot: A life in many dimensions
Another image with a negative scale and rotated folding planes. The picture was part of the exhibition Imaginary in Nuremberg(Form und Formel mathematischer Fantasie) and IMAGINARY: Beauty and power of mathematics
https://www. imaginary.org/gallery/exhibition-beauty-and-power-of-mathema…
An unrotated Mandelbox at a scale of -2,5. Shape was developed in Mandelbulber, ported to Mandelbulb3d and rendered in M3d MC renderer. Part of Maniac Art, Galerie Schauraum Worms
the derivations
Meanwhile, there are countless modifications of the Mandelbox, which reproduce the concept in a different form with different additional parameters or other folding methods.Here I will only present one of the ‒ geometrically as well as artistically ‒ most interesting approaches.
Amazing Surface is based on a proposal by Pablo Andreoli (aka Kali) and is ‒ to put it simply ‒ a somewhat extended 2d Madelbox. All folds are limited to two axes, only the folding planes can be rotated 3-dimensionally. Unfortunately, at this point we leave the realm of exact mathematics. The implementations in different software do not lead to directly comparable results - partly due to the principle (e. g. programmes execute non-commutative rotations in different order).
Submitted by Uli Gaenshirt on
Gezeigt werden großformatige mathematische Bilder, interaktive Software-Exponate, hands-on Objekte, ein quasiperiodisches Puzzle, Filme und illustrierte Texttafeln zum Thema Algebraische Flächen, Fraktale, Polyeder, Kristalle, Quasikristalle, Islamische Girih-Ornamente und angewandte Geometrie.
Der Eintritt ist frei.
Kostenlose öffentliche Führungen werden jeweils sonntags (außer am 19. Juni) um 14 Uhr und mittwochs um 18 Uhr angeboten.
Eröffnung: Mittwoch, den 8. Juni, um 20 Uhr
Öffnungszeiten: Di, Do-So 10-18 Uhr, Mi 10-20 Uhr, Mo geschlossen
Lehrerinformationsveranstaltung (ohne Anmeldung) am Freitag, den 10. Juni, um 16:00 Uhr.
Führungen für Schulklassen, empfohlen ab der neunten Klasse, können im Kunst- und Kulturpädagogischen Zentrum der Museen in Nürnberg (KPZ) gebucht werden:
E-mail: schulen[at]kpz-nuernberg.de Tel: 0911 1331 241
Veranstalter: KOMM-Bildungsbereich im Künstlerhaus
Tel.: 0911 231 14678 oder 0911 231 2853
Tue, Thu - So: 10 am - 6 pm
Wed: 10 am - 8 pm
Mo: closed
Opening: Wed, June 8, 8 pm
Submitted by Torsten Stier on
A colaboration with Ulliroyal led to this little music video in November 2012.
The flights at the beginning and the end of this film were developped and rendered during summer 2012 with Mandelbulber. They are simple Juliaboxes with negative scale and rotated folding planes.
The cut scenes in the middle were done during Octobre 2012 as Amazing Surfaces and a few IFSes in Mandelbulb 3d.
Submitted by Torsten Stier on
In his exhibition Torsten Stier guides you to strangely familliar-looking, 3-dimensonal sceneries of the fractal geometry. He created an intuitive access to a relatively new part of mathematics, that otherwise escapes our linearly logic analysis.
Sometimes Torsten´s works are totally abstract and other times almost photorealistic. His images and animations always spark up associations out of the living and non-living nature or architecture and technics. He uses most modern rendering software and is involved in their development as idea provider and software tester since 2010.
This exhibition is focused on high-resolution printed still-frames, of which about 30 are presented in large format and on different media. Besides that a wall chart gives a brief history of fractals from the “math monsters” of the late 19th century to the latest developments in 3D fractaling.
The Vernissage takes place in Bad Schwalbach on March 25 at 7:30 pm in the cafeteria of the district house.
The exhibition will be on view until May 29 on the 2nd floor of the building.
Mo-Fr: 8:00 - 12:00 am
Tue: 2:00 - 6:00 pm
Submitted by IMAGINARY on
Submitted by Torsten Stier on
Pure entertainment video with a mathematical touch.
Most of the clips base on the amazing surf formula, a derivation of the mandelbox, which starts out with a 2 dimensional membrane, to apply 3d transformations to it. One clip is a mandelbox, one clip is a 3d Kaleidoscopic IFS and one is pseudo kleinian hybrid.
Remarkable is, that it is completely implemented in open source software - including the motion tracking for the intro.
Tools were:
and several other software - a complete list can be found in the credits at the end of the movie
Submitted by Torsten Stier on
A video installation will show all my fractal movies in an endless loop. The folloing artists will show their works here:
Andreas Weingärtner, “Reconformed Creatures” - Sculptures
Patrick Dickescheid, “Psychedelic Drip Art, Cellular Struktures, abstract expressionism” black light art
Christof Dollwet, “Lightwave Worlds” - black light art
Torsten Stier, “borderlands of math” - algorithmic art
