Mandelbrot? Never heard of him
Before anybody knew Mandelbrot, artists were seeing fractals in nature and transfered the patterns in painting, design and sculpture. Fractals, as you know, are geometric patterns that are repeated on smaller and smaller scales to produce intricate designs outside the scope of classical geometry. They are described by a Mandelbrot equation.
The mind has always had a fixation with recursive and fractal patterns,
largely because our environment is filled with them. Only in the last 40 years
have we been able to finally describe this exquisitely subtle math of interacting patterns. Fractals may have become a cliche in modern computer graphics, but they have a long and rich history in art:
1. Medieval Celtic Book of Kells (597 A.D.)
This cultural treasure contains every variety of design typical of Irish art at its best. The most characteristic ornaments of the Book of Kells, as of other illuminated Irish manuscripts of the period, are the closely coiled spirals connected with each other by a number of curves and terminating in the so-called "trumpet fractal pattern".
2. Fractals have a rich history in African Design:
- fractals in typical Ethiopian ornaments;
in village architecture:
and even in traditional hair-style!
Ron Eglash, a professor of comparative studies at Ohio State University, demonstrates the principle with a tool on his Web site with which everyone can create their own computer-generated graphics simulating the fractal branching patterns found in braided hairstyles.
"At first I thought it was just from unconscious social dynamics," Mr. Eglash says, "but during my fieldwork, I found that fractal designs also appear in a wide variety of intentional designs -- hairstyling, textiles, sculpture, painting, carving, metalwork -- and the recursive process of fractal algorithms are even used in African quantitative systems."
(Source article)
3. Persian & traditional Islamic ornaments
Essentially a study in symmetry, extended and enhanced with multiple iterations:
"Persian Rug" examples, created on the computer by applying recursion fractal algorythms:
(Source article)
4.The Italian Renaissance & Dutch Masters
Space Filling by Iteration:
Leonardo da Vinci in his famous Treatise of Painting gave examples of what now is called Leonardo method or blotting method - it emphasized power of "messy forms" like stains on old walls, clouds or muddy water in "favoring mind on various discoveries".
The Dutch painter Jan Van Goyen (1596-1656) was capable of getting out a picture with "small efforts" from stains of colors. Compare Van Goyen's painted clouds with the typical fractal computer-generated "cloud":
Left: Van Goyen, Two Men on a Footbridge over a Stream, 1655, oil on panel (detail); Right: The "cloud" generated by Iterated Function System.
(Source article)
This technique is based on a well-known mathematical algorithm: space filling curve pre-fractals
An interesting application of space filling curves in computer graphics is "half-toning" and dithering of the images:
(Source article)
5. Fractals in Spiritual Art
It's only fitting that the representations of fractals and therefore INFINITY most frequently appear in human art of the Religious and Spiritual varieties:
Islam:
Fractals seem to a distinct element in most world religion's symbolic style:
Egyptian
Judaic
Hindu
Sources: Fractal.50g
Before anybody knew Mandelbrot, artists were seeing fractals in nature and transfered the patterns in painting, design and sculpture. Fractals, as you know, are geometric patterns that are repeated on smaller and smaller scales to produce intricate designs outside the scope of classical geometry. They are described by a Mandelbrot equation.
The mind has always had a fixation with recursive and fractal patterns,
largely because our environment is filled with them. Only in the last 40 years
have we been able to finally describe this exquisitely subtle math of interacting patterns. Fractals may have become a cliche in modern computer graphics, but they have a long and rich history in art:
1. Medieval Celtic Book of Kells (597 A.D.)
This cultural treasure contains every variety of design typical of Irish art at its best. The most characteristic ornaments of the Book of Kells, as of other illuminated Irish manuscripts of the period, are the closely coiled spirals connected with each other by a number of curves and terminating in the so-called "trumpet fractal pattern".
2. Fractals have a rich history in African Design:
- fractals in typical Ethiopian ornaments;
in village architecture:
and even in traditional hair-style!
Ron Eglash, a professor of comparative studies at Ohio State University, demonstrates the principle with a tool on his Web site with which everyone can create their own computer-generated graphics simulating the fractal branching patterns found in braided hairstyles.
"At first I thought it was just from unconscious social dynamics," Mr. Eglash says, "but during my fieldwork, I found that fractal designs also appear in a wide variety of intentional designs -- hairstyling, textiles, sculpture, painting, carving, metalwork -- and the recursive process of fractal algorithms are even used in African quantitative systems."
(Source article)
3. Persian & traditional Islamic ornaments
Essentially a study in symmetry, extended and enhanced with multiple iterations:
"Persian Rug" examples, created on the computer by applying recursion fractal algorythms:
(Source article)
4.The Italian Renaissance & Dutch Masters
Space Filling by Iteration:
Leonardo da Vinci in his famous Treatise of Painting gave examples of what now is called Leonardo method or blotting method - it emphasized power of "messy forms" like stains on old walls, clouds or muddy water in "favoring mind on various discoveries".
The Dutch painter Jan Van Goyen (1596-1656) was capable of getting out a picture with "small efforts" from stains of colors. Compare Van Goyen's painted clouds with the typical fractal computer-generated "cloud":
Left: Van Goyen, Two Men on a Footbridge over a Stream, 1655, oil on panel (detail); Right: The "cloud" generated by Iterated Function System.
(Source article)
This technique is based on a well-known mathematical algorithm: space filling curve pre-fractals
An interesting application of space filling curves in computer graphics is "half-toning" and dithering of the images:
(Source article)
5. Fractals in Spiritual Art
It's only fitting that the representations of fractals and therefore INFINITY most frequently appear in human art of the Religious and Spiritual varieties:
Islam:
Fractals seem to a distinct element in most world religion's symbolic style:
Egyptian
Judaic
Hindu
Sources: Fractal.50g
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