SIMPLE COMPLICATED

MANDELBROT-SET

Figurales of Mandelbrot

Introduction

1.0     Why mathematics is fascinating to a painter

2.0     Aquarells and descriptions
3.0     B.MANDELBROT -Profiling (his life and work)

3.1     Fractals & Selfsimilarity

3.2     Historic notes

3.3     Fractal Geometry

3.4     Fractal Dimensions

3.5     MANDELBROT-SET (Apfelmännchen )

4.0     Education

4.1     Old & New / Confrontation + (Apsidenmosaic-details)

Appendix

5.0     Draft of the mosaic

5.1     Curriculum vitae

5.2     General notes

End

6.0     Thanks // Literature // Addresses

Introduction

1.0 Why mathematics is fascinating to a painter

2.0 Aquarells and descriptions

(40x50)

We learnt at school to calculate and draw geometric figures like cubes, pyramids etc. Here they are shown on a light-blue background, and between them there is n early hidden, the Mandelbrot-Set!! It exists. LOOK !! There is no perspective,on ly 2-dimensional objects are combined with 3 dimensional-objects. They are like in harmony.

(40x50)

Five geometric figures are suspended on a light -yellow background , near the centre is a blue-red IKOSAEDER while the sphere seems to be a solid 2 dimensional structure. Very strange are the spirals, which resemble tentacles. Linear objects are combined with nonlineare objects.----like in nature.

(40x50)

On the light-red background there are represented two big yellow spirals. Such figures can be found on the borders of Mandelbrot-Set. The bodies of geometric structures become imaginary. Only the basic still remains.--like everywhere yet. During one of my exhibitions I watched some elder viewers who did not understand my paintings despite their interest in the shapes and colours. Explanations were requested to illustrate what is simple and at the same time complicated. Soon I decided to inform myself more about CHAOS -Mathematic and the FRACTALS. Two names: MANDELBROT and KALIKOW are important for my paintings.

3.0 B. MANDELBROT -Profiling (his life and work)

B.MANDELBROT was born in 1924 in Poland (Warsaw), and in 1936 his family emigrated to France. In Paris his uncle Szolem M., Prof. of Mathematics-- at the College de France-- took responsibility for his education. 1947 Diploma- Ecole Polytechnique- Paris 1948 M.S.at the California Institute of Technology 1952 Docteur d'Etat- Paris 1987 joined Yale-University, Prof. of Mathematical Sciences Prof. of Economics, later Applied Mathematics at Havard, than Albert-Einstein College of Medicine 1995 Professeur de L'Academie des Science Ecole Polytechnique. Member of the Americ. Academy of Science and Art, and of the Natural Academy of Science Numerous honorary doctorates and awards. 1993 Wolf Price.in physics Fellow emeritus (Physical Science),at IBM ,T.J.Watson Research Center.N.Y.. There, sitting in a glasehouse, he watched the mountains and created by chance the FRACTALS. B. MANDELBROT is best known as the father of Fractal Geometry.

3.1 Fractals & Selfsimilarity

3.2 Historic notes

3.3 Fractal Geometry

Selfsimilarity

3.4 Fractal Dimensions

To charcterise this selfsimilar complexity Mandelbrot created also the concept of FRACTAL DIMENSION: " If a smooth curve had a dimension of 1 and a smooth surface a fractal dimension of 2 -a coastline could be said to have a fractal dimension somewhere between! The coastline of Britain has a dimension of 1,26. FRACTALS are shapes or behaviours that have similar properties at all levels of magnification or during all times. FRACTALS are a concept that unites clouds, coastlines, plants and chaotic attractors.

Therefore they are evident in engineering, chemical engineering, metallurgy, mathematics, art and even the study of chronic illness and health. For instance,in the past decade studies have shown that the healthy heart beats with a fractal rhythm- and that a nearly periodic heartbeat is a symptom of impending cardiac arrest. Diabetics,too, has been shown to have a fractal aspect as the fluctuations in glucose levels in a diabetic have a fractal spectrum. Mandelbrot says: " I explored them further and used them in many contexts from finances to galaxies " and " my main tool of thought remained the eye.------and I am powered by the unanticipated possibility of transforming the nearly developed computer into a visual helper of mathematics, sciences and also ART. " ART is one of the few forms of human productivity which causes no destruction and brings no catastrophes because it is life.

Hinterglasbild

3.5 MANDELBROT SET (Apfelmännchen )

Clouds are not like a sphere /// Mountains are not coneshaped /// Coastlines are not circles /// Barks of trees are not smooth /// lightnings are not linear. Only crystals have an ordered structure --no chaos -but the surrounding materials have not. Is TIME also an attractor with selfsimilarity,and is history an iterating and noniterating process? When analysing the MANDELBROT-Set there are figurales like tentacles.

Generations of mathematicians, computer-experts and even artists were challenged to study these fascinating structures. Still in the 80s the computer was nearly unknown and mysterious. All of a sudden the development of the home and personal computers set in. Nowadays we often find them in living-and children's rooms and they are important tools all around the world. Using a computer now belongs to the basic knowledges as reading, writing and calculating. Since the introduction of the MANDELBROT -Set- in German named "Apfelmännchen" these complex phenomena could be created and described by simple rules iterated over and over again. In the meantime there are about 50.000 publications related to this subject, but how many by artists?

4.0 Education

4.1 Old & New / Confrontation + (Apsidenmosaic-details ROMA 4. century)

Pointing hands

The computer specialist Dan Kalkow said: " A Computer makes things visible" And "The Mandelbrot-Set always existed."". Another specialist of the Mandelbrot-Set, Prof. J.H.Hubbard (Dep. of Mathematics, Cornell University, Ithaca N. Y. 14853), continued together with Prof H.O.Peitgen (University Bremen, Dept.of Mathematics ) some experiments.

Appendix

5.0 Draft of the mosaic

view of a section (13x18) golden background (Hinterglasbild)

5.1 Curriculum vitae

I was born in Berlin (Germany), married in 1967 to Innsbruck (Austria). After familylife and some years of profession at the university of Innsbruck, I started in 1986 my painting-hobby. In 1987 member of the Künstlerbund Tirol, in 1997 Bildkunst Österreich S. 692 I attended different schools of art. Voyages to most continents. Since 1997 I have been studying history and art ( Kunstgeschichte) at Innsbruck University. In 1997 Video EINFACH KOMPLIZIERT. In 1999 Internet SIMPLE COMPLICATED.

5.2 General notes

6.0 Thanks // Literature // Addresses

Literature/Addresses BOWEN J. @comlab.ox.ac.uk
BRIGGS, John u.David PEAT : Die Entdeckung des Chaos ,1989, Carl HanserVerlag
DEWDNEY; A. K. Das Apfelmännchen, Spektrum d.Wissenschaften, Comp.Kurzweil Sonderheft 1987
HARPER &ROW "Turbulent mirror" New York.
IBM Corp. Research Homepage 1996, Profiling B.Mandelbrot./ Fractal lead story
IBM Corp. Research 1998, Fractal science.

Conference on a new space for culture and society 19.-23.Nov. 1996 B. Mandelbrot

HUBBARD Prof. John H.Cornell University, Dept. Mathem. ITHACA N.Y. 14853 USA
PEITGEN Prof. Heinz Otto, Univ. Bremen 2800 Bremen 33 Postfach 330440
SILVER Rollo, Box 111 SAN CHRISTOBAL N.M.87564 USA

(aus: Die Presse, Zygmunt Januszewski)