Submitted by Torsten Stier on
기술적인 측면으로는 대부분의 영상은 간단한 Mandelbox 프랙탈입니다. 그 중 일부는 음의 비율을 가지고 있고 접힌 평면이 회전해 있습니다. 프랙탈 영상은 전부 Mandelbulber 1.21 OpenCL과 CPU 모드로 편집되었습니다.
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
On display are large-sized mathematical images, interactive software exhibits, hands-on objects, a quasiperiodic jigsaw, films and illustrated text panels about algebraic surfaces, fractals, polyhedrons, crystals, quasicrystals, Islamic girih-ornaments and applied geometry.
Admission is free.
Free guided tours are schedulled on Sundays (except 19 June) at 2 pm and Wednesdays at 6 pm.
Information meeting for teachers (wthout registration) on Friday, 10 June, at 4 pm.
Guided tours for school classes, recomended for 9th grade and up, can be booked at the Kunst- und Kulturpädagogisches Zentrum der Museen in Nürnberg (KPZ):
E-mail: schulen[at]kpz-nuernberg.de Phone: +49 (0)911 1331 241
Organizer: KOMM-Bildungsbereich im Künstlerhaus
Phone: +49 (0)911 231 14678 or +49 (0)911 231 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
Ulliroyal과의 작업에서 2012년 11월에 이 짧은 뮤직비디오를 만들었습니다. 시작과 끝 부분의 비행 장면은 2012년 여름에 Mandelbulber로 개발되었습니다. 이들은 음수 스케일의 Juliabox들과 회전되어 접혀진 평면들로 이루어져 있습니다.
중간의 컷신은 2012년 10월 Mandelbulb 3d의 Amazing Surfaces와 fewIFSes로 마무리되었습니다.
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
프랙탈에 관련된 영상들이 끝없이 반복되어 틀어질 것입니다. 작품이 전시될 예정인 예술가들은 다음과 같습니다.
Andreas Weingärtner, “Reconformed Creatures” – 조소
Patrick Dickescheid, “Psychedelic Drip Art, Cellular Struktures, abstract expressionism” 자외선 예술
Christof Dollwet, “Lightwave Worlds” – 자외선 예술
Torsten Stier, “borderlands of math” – 알고리즘 예술
