enjoy colorful fashion with great designs from chaos theory and mathematics
fashion and gifts from the realm of chaos
fashion and gifts from the realm of chaos
Beautiful and imaginative motifs - chic clothing for women, men and children! Fashionable gifts and clothing for mathematicians, nerds, artists, physicists, computer scientists, biologists, chemists, natural scientists, engineers.
Created using fractals and chaos theory. Exclusive designs, unique watercolors and graphics!
Fashion - Clothing - T-Shirts - Sportswear - Tops - Organic Products
Children's and baby clothing
Sweaters and hoodies
Cups - mugs - drinking bottles
Bags - backpacks
Men's sweaters and hoodies
Men's sweaters and hoodies
Fashionable sweaters and hoodies for men! Chic sweatshirts and pullovers for teenagers, mathematicians, craftsmen, artists, nerds, physicists, computer scientists, engineers, biologists, chemists, natural scientists.
Sweater created with fractals and motifs from chaos theory.
Strange attractors and exclusive designs on men's sweatshirts.
Great designs on men's clothing!
Mathematics at your fingertips!
Math to wear!
Men's long sleeve shirts
Men's long sleeve shirts
Mathematics to wear and to touch for men!
Fractals and motifs from chaos theory give the sweaters their special character!
Strange attractors and exclusive designs on men's long sleeve shirts.
Fashionable long-sleeved shirts for men! Chic long-sleeved shirts for nerds, teenagers, mathematicians, craftsmen, artists, scientists, young people, physicists, computer scientists, educators, chemists.
Gorgeous designs on men's clothing!
Men - jackets and vests
Men - jackets and vests
Colorful artistic designs on jackets and vests for men.
Motifs from chaos theory and strange attractors on sporty jackets or vests.
Chic jackets for men! Fashionable vests for young people, computer scientists, nerds, nurses, teenagers, mathematicians, craftsmen, artists, physicists, computer scientists, lecturers, biologists, chemists, kindergarten teachers, natural scientists, educators, engineers, professors, educators.
Mathematics to wear and feel!
Men's polo shirts
Men's polo shirts
Great designs from chaos theory on polo shirts!
Artistic watercolors from the chaos on men's clothing!
Unusual motifs with a mathematical background on polo shirts.
Top fashionable polo shirts for men! Smart polo shirts for scientists, teenagers, mathematicians, craftsmen, educators, nerds, artists, professors, physicists, computer scientists, chemists, engineers, lecturers, kindergarten teachers, professors.
Mathematics to wear and feel!
Men's tank tops
Men's tank tops
Hot fashion on tank tops from chaos theory!
Chic tank tops for men! Cool tank tops for nurses, mathematicians, craftsmen, nerds, educators, artists, teenagers, physicists, young people, computer scientists, chemists, natural scientists, pastors, engineers, doctors, biologists, construction workers, trainees, kindergarten teachers, professors.
Artistic designs with a math background on hot shirts!
Mathematics you can feel!
Men's organic products
Men's organic products
Men's natural products with motifs from chaos theory.
Exclusive motifs on men's clothing made from organic products - created with strange attractors.
Chic men's clothing made from natural products for nerds, nurses, mathematicians, craftsmen, artists, teenagers, physicists, educators, computer scientists, chemists, natural scientists, pastors, engineers, doctors, construction workers, trainees, kindergarten teachers, professors.
Mathematical fashion to feel good!
Organic products from the chaos
Men sportswear
Men sportswear
Men's sportswear with fantastic designs from chaos theory!
Dynamic men's sportswear: created with fractals of dynamic systems!
Chic men's sportswear - sportswear natural scientists, teenagers, teachers, biologists, mathematicians, craftsmen, geriatric nurses, nerds, artists, professors, physicists, computer scientists, educators, engineers, lecturers, kindergarten teachers, professors.
Men's sports gear with beautiful motifs from the chaos!
Men's workwear
Men's workwear
Men's work clothes with artful designs from chaos theory!
Men's work clothes made from strange attractors!
Fashionable men's workwear for mathematicians, craftsmen, nerds, construction workers, artists, physicists, computer scientists, parishes, biologists, chemists, natural scientists, engineers, geriatric nurses.
Men’s work clothes with exclusive motifs from the chaos.
Colorful work dress for the stressed man!
Men's t-shirts
Men's t-shirts
Men's t-shirts with artistic watercolors from the chaos!
Colorful men's sweatshirts with imaginative designs from chaos theory!
Top fashionable men's shirts! Chic T-shirts for kindergarten teachers, mathematicians, craftsmen, teenagers, nerds, artists, physicists, computer scientists, pastors, biologists, chemists, scientists, engineers.
Mathematical men's fashion to feel and wear!
Exclusive men's jerseys with great designs and beautiful motifs!
Accessories - bandanas
Accessories - bandanas
Fashionable bandanas and scarves! Chic headbands and scarves for teenagers, mathematicians, craftsmen, nerds, artists, physicists, construction workers, computer scientists, farmers, biologists, chemists, natural scientists, engineers.
Headscarves created with fractals and curves from chaos theory.
Strange attractors and exclusive designs on bandanas.
Extraordinary designs on multifunctional towels!
Math to wear!
Mathematics at your fingertips!
Accessories - cups and mugs
Accessories - cups and mugs
Fashionable cups and mugs for mathematicians, craftsmen, teenagers, nerds, artists, physicists, farmers, computer scientists, biologists, chemists, scientists, engineers.
Pots and cups with unusual designs from the chaos!
Mathematics to enjoy from chic drinking cups!
Special drinking vessels with extraordinary images and fractals from mathematics!
Accessories - caps and hats
Accessories - caps and hats
Exclusive designs on hats and caps!
Smart kappies and caps for athletes, teenagers, mathematicians, craftsmen, nerds, young people, artists, physicists, construction workers, computer scientists, geriatric nurses, farmers, biologists, golfers, educators, scientists, kindergarten teachers, engineers, teachers, hairdressers, architects .
Strange attractors from chaos theory on sporty caps and hats!
Fashionable math to wear!
Accessories - phone and tablet cases
Accessories - phone and tablet cases
Noble designs on mobile phone and tablet cases!
Nice motifs from chaos theory on mobile phone covers!
Fashionable mobile phone and tablet cases for nerds, teenagers, mathematicians, craftsmen, architects, young people, artists, bank employees, physicists, construction workers, computer scientists, geriatric nurses, farmers, professors, biologists, chemists, educators, natural scientists, kindergarten teachers, engineers, teachers, Hairdressers, lecturers.
Math while calling!
Accessories - pillows
Accessories - pillows
Nice patterns on pillows!
Fashionable sofa cushions for nerds, artists, teenagers, mathematicians, architects, young people, educators, physicists, construction workers, computer scientists, geriatric nurses, farmers, professors, biologists, chemists, educators, scientists, kindergarten teachers, engineers, teachers, hairdressers, craftsmen , Lecturers, bank employees.
Mathematical motifs from chaos theory on cuddly pillows!
Math to cuddle in the living room!
Accessories - cuddly toys
Accessories - cuddly toys
Stuffed animals for children with cheerful patterns!
Cuddly bears with funny designs from chaos theory!
Teddies and cuddly bears for nerds, kindergarten teachers, artists, mathematicians, architects, young people, educators, physicists, construction workers, computer scientists, geriatric nurses, professors, biologists, chemists, educators, natural scientists, teenagers, engineers, teachers, hairdressers, Farmers, artisans, lecturers, bank employees.
Mathematics to smooch!
Accessories - Mousepad
Accessories - Mousepad
Mousepads with chic designs out of the chaos!
Mousepads for nerds, artists, mathematicians, architects, engineers, young people, bank employees, educators, physicists, kindergarten teachers, computer scientists, geriatric nurses, professors, biologists, chemists, educators, natural scientists, teenagers, teachers, craftsmen, lecturers.
Documents for the computer mouse with breathtaking images from mathematics!
Nice math to work with the computer mouse!
Accessories - aprons
Accessories - aprons
Aprons with colorful watercolors from the chaos!
BBQ aprons with imaginative designs from mathematics!
Highly fashionable kitchen and cooking aprons for female nerds, mathematicians, kindergarten teachers, teenagers, craftswomen, artists, physicists, farmers, computer scientists, nurses, biologists, chemists, scientists, engineers.
Bib aprons with exclusive designs!
Math in the kitchen!
Accessories - stickers
Accessories - stickers
Stickers and decals with really cool designs from chaos theory!
Chic badges and stickers for nerds, mathematicians, architects, kindergarten teachers, artists, young people, educators, physicists, computer scientists, nurses, professors, biologists, chemists, educators, natural scientists, teenagers, engineers.
Labels and labels with noble motifs from the chaos!
Eye-catching adhesive labels with a mathematical background!
Mathematics immortalized on stickers!
Accessories - cloth masks
Accessories - cloth masks
Cloth masks with chaos theory!
Protective masks for teenagers, nerds, mathematicians, architects, kindergarten teachers, artists, teenagers, educators, physicists, computer scientists, professors, biologists, chemists, educators, construction workers, natural scientists, teenagers, engineers, academics, technicians.
Face masks with selected motifs from the chaos!
Chaos theory on protective masks against viruses and bacteria!
Accessories - sports bags
Accessories - sports bags
Sports bags with elegant designs from chaos theory!
Bags and sports bags for female nerds, mathematicians, athletes, soccer players, craftswomen, artists, physicists, geriatric nurses, computer scientists, doctors, biologists, chemists, scientists, engineers.
Fabric bags with chic designs from the chaos!
Fashionable handbags with math!
Accessories - backpacks and travel bags
Accessories - backpacks and travel bags
Backpacks with exciting designs from chaos theory!
Travel bags and rucksacks for hikers, nerds, mountaineers, mathematicians, adventurers, climbers, artists, athletes, programmers, physicists, travelers, computer scientists, biologists, chemists, scientists, engineers.
Travel bags with selected motifs from the chaos!
Math for Travel!
Accessories - drinking bottles
Accessories - drinking bottles
Drinking bottles with colorful patterns from chaos theory!
Drinking bottles for cyclists, soccer players, mountain hikers, nerds, handball players, mountaineers, volleyball players, mathematicians, climbers, artists, athletes, programmers, physicists, computer scientists, biologists, chemists, natural scientists, engineers.
Bottles with selected pictures from the chaos!
Math against thirst!
Accessories - enamel cups
Accessories - enamel cups
Enamel mugs with colorful fractals from the chaos!
Enamel cups and enamel pots for campers, campfires, mathematicians, camps, coffee parties, tea parties, nerds, artists, physicists, computer scientists, biologists, kindergarten teachers, chemists, natural scientists, engineers.
Enamel mug with amazing graphics from the mess!
Mathematics for drinking coffee and tea!
Accessories - buttons and badges
Accessories - buttons and badges
Buttons and badges with unique patterns from the chaos!
Buttons and plaques for teenagers, children, nerds, mathematicians, architects, computer scientists, kindergarten teachers, artists, young people, educators, physicists, nurses, professors, biologists, chemists, educators, scientists, lecturers, engineers.
Stickers with the unknown graphics from the chaos!
Buttons with math!
Women sweaters and hoodies
Women sweaters and hoodies
Fashionable sweaters and hoodies for women! Chic sweatshirts and pullovers for mathematicians, craftsmen, nerds, kindergarten teachers, artists, physicists, computer scientists, biologists, teachers, chemists, natural scientists and engineers.
Sweater created with fractals and motifs from chaos theory.
Strange attractors and exclusive designs on women sweatshirts.
Great designs on women's clothing!
Mathematics at your fingertips!
Women long sleeve shirts
Women long sleeve shirts
Gorgeous designs on women's clothing!
Fractals and motifs from chaos theory give sweaters their special charm!
Fashionable long-sleeved shirts for women! Chic long-sleeved shirts for nurses, mathematicians, craftswomen, nerds, artists, physicists, pedagogues, computer scientists, construction workers, biologists, professors, scientists, engineers.
Mathematics to wear and to touch!
Women - jackets and vests
Women - jackets and vests
Colorful artistic designs on jackets and vests for women.
Motifs from chaos theory and strange attractors on sporty jackets or vests.
Chic jackets for women! Fashionable vests for geriatric nurses, mathematicians, craftswomen, nerds, artists, physicists, hairdressers, computer scientists, biologists, saleswomen, chemists, scientists, engineers.
Mathematics to slip in and feel!
Women polo shirts
Women polo shirts
Great designs from chaos theory on polo shirts!
Artistic watercolors from the chaos on women's clothing!
Unusual motifs with a mathematical background on polo shirts.
Top fashionable polo shirts for women! Smart polo shirts for speech therapists, mathematicians, craftswomen, nerds, artists, physicists, teachers, computer scientists, biologists, chemists, scientists, engineers.
Mathematics to put on and slip on!
Women tank tops
Women tank tops
Hot fashion on tank tops from chaos theory!
Chic tank tops for women! Cool tank tops for teenagers, mathematicians, craftswomen, nerds, artists, physicists, nurses, computer scientists, biologists, doctors, physiotherapists, natural scientists and engineers.
Artful designs with a mathematical background on hot shirts!
Mathematics to slip on and touch!
Women organic products
Women organic products
Women natural products with motifs from chaos theory.
Exclusive motifs on women's clothing made from organic products - created with strange attractors.
Chic women's clothing made from natural products for mathematicians, craftsmen, nurses, nerds, artists, physicists, hairdressers, computer scientists, biologists, chemists, scientists, engineers.
Mathematical women's fashion to feel good!
Women sportswear
Women sportswear
Women's sportswear with fantastic designs from chaos theory!
Women sportswear with math background.
Chic women's sportswear - sportswear for mountaineers, mathematicians, craftswomen, nerds, artists, nurses, physicists, computer scientists, biologists, chemists, scientists, engineers.
Women's sportswear with beautiful motifs from the chaos!
Women workwear
Women workwear
Women's work clothes with artful designs from chaos theory!
Women's work clothes created with weird messy attractors!
Fashionable women work clothes for construction workers, mathematicians, craftswomen, nerds, artists, carpenters, physicists, computer scientists, nannies, architects, scientists, engineers.
Colorful work dress for the stressed woman!
Women t-shirts
Women t-shirts
Women's t-shirts with artistic watercolors from the chaos!
Colorful women's sweatshirts with imaginative designs from chaos theory!
Top fashionable women shirts! Chic T-shirts for hairdressers, mathematicians, craftswomen, nerds, artists, carpenters, physicists, computer scientists, biologists, chemists, nurses, natural scientists, engineers.
Experience mathematical women's fashion!
Cases - Samsung cases
Cases - Samsung cases
Noble designs on Samsung cases!
Unique items from chaos theory on Samsung protective covers!
Fashionable Samsung covers for nerds, artists, computer scientists, teenagers, mathematicians, architects, young people, pedagogues, physicists, educators, natural scientists, kindergarteners, construction workers, geriatric carers, farmers, professors, biologists, chemists, engineers, teachers, hairdressers, Craftsmen, lecturers.
Math on Cell Phones!
Cases - Samsung Cell Phone Cases
Cases - Samsung Cell Phone Cases
Selected designs on Samsung cell phone cases!
Single pieces from chaos theory on Samsung protective covers!
Smart Samsung covers for artists, female nerds, computer scientists, teenagers, technicians, mathematicians, math teachers, craftswomen, psychologists, physicists, doctors, biologists, hairdressers, chemists, scientists, engineers.
Math design on phones!
Cases - Samsung Cell Phone Cases
Cases - Samsung Cell Phone Cases
Unique designs on Samsung cell phone cases!
Unique items from the chaos on Samsung cases!
Selected Samsung cases for nerds, mathematics professors, mathematics teachers, computer science teachers, IT specialists, physics teachers, physics professors, mathematics students, computer science professors, computer science students, physics students, mathematics lecturers.
Chaotic designs on cell phone cases!
Cases - Samsung Mobile Phone Cases
Cases - Samsung Mobile Phone Cases
Unusual designs on Samsung cell phone cases!
Visualized algorithms from chaos theory on Samsung cases!
Selected Samsung cases for scientists, IT lecturers, physics lecturers, art scholars, academics, futurologists, pedagogues, nerds, computer geeks, students, lecturers, programmers, art lovers, trainee teachers.
Abstract Art on Cell Phone Cases!
Cases - iPhone cases
Cases - iPhone cases
Noble designs on iPhone cases!
Unique items from chaos theory on iPhone cases!
Fashionable iPhone cases for nerds, artists, computer scientists, teenagers, mathematicians, architects, young people, educators, physicists, educators, natural scientists, kindergarten teachers, construction workers, geriatric nurses, farmers, professors, biologists, chemists, engineers, teachers, hairdressers, Craftsmen, lecturers.
Chaos on Cell Phones!
Cases - iPhone cell phone cases
Cases - iPhone cell phone cases
Selected Patterns on iPhone Cell Phone Cases!
Exclusive single pieces from chaos theory on iPhone cases!
Chic iPhone cases for artists, female nerds, computer scientists, teenagers, technicians, mathematicians, math teachers, craftswomen, psychologists, physicists, doctors, biologists, hairdressers, chemists, scientists, engineers.
Math design on mobile phones!
Cases - iPhone mobile phone cases
Cases - iPhone mobile phone cases
Extraordinary designs on iPhone mobile phone cases!
Visualized computer algorithms from chaos theory on iPhone cases!
Selected iPhone cases for nerds, math professors, math teachers, computer science teachers, IT specialists, physics teachers, physics professors, math students, computer science professors, physics students, math lecturers.
Abstract artwork on cell phone cases!
Cases - iPhone mobile phone cases
Cases - iPhone mobile phone cases
Beautiful designs on iPhone cases!
Unique items from the theory of chaos on iPhone cases!
Selected iPhone cases for scientists, computer science lecturers, physics lecturers, art scholars, academics, futurologists, educators, nerds, computer geeks, students, lecturers, programmers, art lovers, trainee teachers.
Designs from chaos theory on cell phone cases!
Children and Babies - Baby Bodysuits
Children and Babies - Baby Bodysuits
Colorful baby bodysuits with funny designs!
Colorful and imaginative baby rompers!
Baby rompers with great colors!
Baby suits for new mothers and fathers!
Baby gifts and souvenirs from grandmas, fathers, grandpas, uncles, friends, godparents, grandfathers, greatomas, grandmothers, aunts, great-grandparents.
Children and babies - baby long sleeve shirts
Children and babies - baby long sleeve shirts
Infant long sleeve shirts created with fractals and motifs from chaos theory.
Strange attractors and exclusive designs on long sleeve shirts for newborns!
Great designs on kids clothes!
Fashionable baby long sleeve shirts for new mothers and fathers!
Fashionable baby gifts from great-grandmothers, grandmothers, aunts, acquaintances, grandmas, fathers, grandpas, uncles, friends, godparents, grandfathers, great-grandparents.
Baby accessories
Baby accessories
Colorful artistic designs on baby accessories for the happy baby!
Motifs from chaos theory and strange attractors on toddler accessories.
Chic infant accessories! Fashionable newborn accessories for the happy parents!
Mathematics to slip in and feel!
Children and babies - baby bibs
Children and babies - baby bibs
Great designs from chaos theory on baby bibs!
Artistic watercolors from the chaos on toddler bibs!
Unusual motifs with math background on infant bib.
Top fashion bibs for newborns! Chic baby bibs for new parents!
Mathematics to put on and slip on!
Children and babies - baby hats
Children and babies - baby hats
Fashion on baby hats from chaos theory!
Chic toddler hats! Cool infant hats for fish-baked fathers and mothers!
Ornate designs with a math background on baby hats!
Mathematics to put on and feel!
Top fashion designs out of the chaos!
Children and Babies - Baby T-Shirts
Children and Babies - Baby T-Shirts
Baby t-shirts with images from chaos theory.
Exclusive motifs on baby shirts - created with strange attractors.
Chic baby jerseys - gifts from grandmas and grandpas!
Cool baby sweatshirts made with mathematical knowledge!
Mathematical fashion to feel good!
Children and babies - organic products
Children and babies - organic products
Baby organic products with fantastic designs based on chaos theory!
Dynamic baby natural products: created with fractals of dynamic systems!
Chic baby clothes made from organic products - souvenirs for aunts, uncles, grandfathers and grandmothers!
Baby clothes made from natural products with beautiful graphics from the chaos!
Children and babies - long sleeve shirts
Children and babies - long sleeve shirts
Baby long-sleeved shirts with artistic watercolors out of the chaos!
Colorful long-sleeved baby shirts with fantastic patterns from chaos theory!
Top fashionable children's long-sleeved shirts! Chic long-sleeved shirts for newborns!
Exclusive children's long-sleeved shirts with great designs and beautiful motifs!
Experience mathematical children's fashion!
Children and babies - long sleeve shirts
Children and babies - long sleeve shirts
Baby long-sleeved shirts with artistic watercolors out of the chaos!
Colorful long-sleeved baby shirts with fantastic patterns from chaos theory!
Top fashionable children's long-sleeved shirts! Chic long-sleeved shirts for newborns!
Exclusive children's long-sleeved shirts with great designs and beautiful motifs!
Experience mathematical children's fashion!
Children and babies - sweaters and hoodies
Children and babies - sweaters and hoodies
Baby sweaters and hoodies with beautiful images from the universe of chaos!
Children and toddler sweaters with exclusive pictures!
Sweaters for babies and toddlers from grandma and grandpa!
Top fashion baby sweatshirts!
Children and Babies - T-Shirts
Children and Babies - T-Shirts
Colorful kids shirts, kids jerseys with cheerful colors!
Funny kids sweatshirts out of the chaos!
Children's fashion from chaos theory!
Exclusive fashion designs for children from the world of mathematics!
Happy fashion for happy children!
Murals and posters
Murals and posters
Abstract designs from chaos theory on posters and murals!
Unique items from the world of chaos on posters!
Wonderful posters from the world of chaos - for nerds, artists, computer scientists, teenagers, mathematicians, architects, young people, educators, physicists, educators, natural scientists, kindergarten teachers, geriatric nurses, farmers, professors, biologists, chemists, engineers , Teachers, hairdressers, craftsmen, lecturers.
Unique math on posters and murals!
Posters and murals
Posters and murals
Selected designs on posters and murals!
Single pieces from chaos theory on murals!
Exclusive posters for artists, female nerds, computer scientists, teenagers, technicians, mathematicians, math teachers, craftsmen, psychologists, physicists, doctors, biologists, hairdressers, chemists, scientists, engineers.
Math design on posters and murals!
Posters and murals
Posters and murals
Unique pictures from chaos theory on posters!
Unique items from the chaos on posters and murals!
Imaginative posters for children, nerds, math professors, math teachers, computer science teachers, IT specialists, physics teachers, physics professors, math students, computer science professors, computer science students, physics students, math lecturers.
Chaotic designs on posters!
Murals and posters
Murals and posters
Unusual designs on posters and murals!
Visualized algorithms from chaos theory on posters!
Selected beautiful murals for scientists, IT lecturers, physics lecturers, art scholars, academics, futurologists, educators, nerds, computer geeks, students, lecturers, programmers, art lovers, trainee teachers.
Abstract math art on posters!
Poster and wall painting
Poster and wall painting
Extraordinary mathematical wall painting on posters!
Visualized computer algorithms from chaos theory on posters!
Sensational posters from the chaos for children, programmers, educators, art lovers, scientists, educators, female nerds, female computer freaks, teachers, teenagers, lecturers.
Abstract works of art from mathematics on murals and posters!

Small T-shirt gallery

Mathematical Background

How does the creation of the designs actually work?

Simple math formulas ...

In principle, very simple mathematical formulas were used to generate the designs.

These are simple equations that begin with a pair of starting values x (0) | y (0).

The next pair of values x (1) | y (1) is then calculated from this, and from this the next pair of values x (2) | x (2).

This continues hundreds of millions of times.

For example, one calculates one billion x | y points - so we get:

x(0)|y(0)

x(1)|y(1)

x(2)|y(2)

x(3)|y(3)

...

x(1.000.000.000)|y(1.000.000.000) 

Counting and coloring ...

The calculated x | y points are then more or less densely scattered on an x-y plane. This level is then divided into a grid of, for example, 1000 x 1000 points. You get a grid with 1,000,000 squares or pixels.

And now comes the really first simple ingenious trick that leads to the wonderful fractals: you COUNT how many of the calculated x|y points are in a grid point or pixel (you count the "hits", so to speak). In this way one then obtains pixels (grid locations on the x|y plane) in which no, few, many or very many calculated points (hits) lie.

This then results in a scale from 0 to, for example, a maximum of 100,000 values found in a grid square or pixel. The second nice trick is to give the scale values colors: e.g. You color a pixel with 0 to 10 hits with white, with 11 to 1000 hits red, with 1001-10000 hits green, with 10001-100000 hits blue.

Well chosen starting values and parameters + good coloring strategy ...

With a little "luck" you will have a good pair of starting values and, above all, the right parameters. With a good “coloring strategy”, you will get graphics that look like the designs in sali-math-arts.

Lots of attempts to find the right parameters ...

By the way, it can happen that you need hundreds of billions of attempts just to find suitable parameters that should lead to beautiful designs. Some of the calculated designs took a few days or weeks of uninterrupted calculations.

Which designs are "good" ...

But how do you determine whether parameters are actually candidates for a design to be "good"? The simplest criterion for whether a design is worth seeing was initially to determine whether the parameters and starting values used "generate" enough hits for pixels. The "most" attempts namely scatter the hits very far into individual pixels of the x|y plane, so that "apart from a fog with individual points one cannot see anything" - they are therefore useless.

The "art" therefore also and above all consists in actually initially finding parameters that lead to "visible" results. A further step then consists in the admittedly subjective optical selection of "beautiful designs" from the visible candidates.

New equations for new design types ...

In the literature you can find a multitude of well-known equations from chaos theory and from the world of strange attractors and fractals, the skillful parameterization of which - as described above - already leads to a certain range of different graphic characteristics for each type of equation. I also used such equations and - as mentioned - determined suitable parameters with sometimes considerable computing effort in order to obtain different designs.

However, in order to find completely new design types, parameter variations alone are not enough. I therefore modified existing types of equations on the one hand, and set up new types of equations on the other in order to find new design types and designs.

Equations that come from my own pen or that I have modified or expanded from existing ones always contain the abbreviation SALI in the name. All the others come from well-known sources that I found one after the other, for example on relevant Python sites, in Wikipedia or in books on chaos, fractals or non-linear dynamic systems.

Chic designs with a mathematical background from chaos theory give fashion and gifts their very own special charm!

x(i) := f(x(i-1)|y(i-1))
y(i) := g(x(i-1)|y(i-1))

Clifford

x(i) = sin(a * y(i-1)) + c * cos(a * x(i-1))
y(i) = sin(b * x(i-1)) + d * cos(b * y(i-1))

Clifford Designs

Bedhead

x(i) = sin(x(i-1)*y(i-1)/b)*y(i-1) + cos(a*x(i-1)-y(i-1))

y(i) = x(i-1) + sin(y(i-1))/b

Bedhead Designs

Gumowsky Mira

x(i) = y(i-1) + a*(1 - b*y(i-1)**2)*y(i-1) + G(x(i-1), mu)
y(i) = -x(i-1) + G(x(i), mu)


G(x, mu) = mu * x + 2 * (1 - mu) * x**2 / (1.0 + x**2)

Gumowsky Mira Designs

Symmetric Icon

zzbar(i) = x(i-1)*x(i-1) + y(i-1)*y(i-1)
p(i) = a*zzbar(i) + l
zreal(i) = x(i)
zimag(i) = y(i)

for k in range(1, d-1):
za(i) = zreal(i) * x(i) - zimag(i) * y(i)
zb(i) = zimag(i) * x(i) + zreal(i) * y(i)
zreal(i) = za(i)
zimag(i) = zb(i)

zn(i) = x(i)*zreal(i) - y(i)*zimag(i)
p(i) = p(i) + b*zn(i)

x(i) = p(i)*x(i-1) + g*zreal(i) - om*y(i-1)
y(i) = p(i)*y(i-1) - g*zimag(i) + om*x(i-1)

Symmetric Icon Designs

Symmetric Icon SALI_1

zzbar(i) = x(i-1)*x(i-1)+cos(y(i-1))*cos(y(i-1)) + y(i-1)*y(i-1) + cos(x(i-1))*cos(x(i-1))
p(i) = a*zzbar(i) + l
zreal(i) = x(i)
zimag(i) = y(i)

for k in range(1, d-1):
za(i) = zreal(i) * x(i) - zimag(i) * y(i)
zb(i) = zimag(i) * x(i) + zreal(i) * y(i)
zreal(i) = za(i)
zimag(i) = zb(i)

zn(i) = x(i)*zreal(i) - y(i)*zimag(i)
p(i) = p(i) + b*zn(i)

x(i) = p(i)*x(i-1) + g*zreal(i) - om*y(i-1)
y(i) = p(i)*y(i-1) - g*zimag(i) + om*x(i-1)

Symmetric Icon SALI_1 Designs

Jason Rampe Sali 1

x(i) = (cos(y(i-1)*b)+c*sin(x(i-1)*b))*e
y(i) = (cos(x(i-1)*a)+d*sin(y(i-1)*a))*f

Jason Rampe Sali 1 Designs

Svensson

x(i) = d * sin(a * x(i-1)) - sin(b * y(i-1))
x(i) = c * cos(a * x(i-1)) + cos(b * y(i-1))

Svensson Designs

Hopalong 2

x(i) = y(i-1) - 1.0 - sqrt(fabs(b * x(i-1) - 1.0 - c)) * sign(x(i-1) - 1.0)
y(i) = a - x(i-1) - 1.0

Hopalong 2 designs

Fractal Dream

x(i) = sin(y(i-1)*b)+c*sin(x(i-1)*b)
y(i) = sin(x(i-1)*a)+d*sin(y(i-1)*a)

Fractal Dream designs

more equations will follow ... in progress

About "sali-math-arts" Europe - the special gift.

Dear visitors, welcome to our small mathematical art gallery!

Mathematical art, art with fractals, art with chaos theory

This WEB page gives you an unusual look into the magical world of chaos-theoretical fractals!

How did this website come about?


Some time ago, for fun, I had a fancy chaos-theoretical graphic printed on a T-shirt.This seemingly piqued the curiosity of a few friends who found this t-shirt eye-catching and inspiring.
So I came up with the idea of ​​printing T-shirts with selected fractals as fashionable motifs and offering them to an interested public.


Other gifts and clothing were added and are now also offered with unusual print designs from chaos theory.


This is how the idea of ​​the online shop sali-math-arts - the special gift was born.


With selected fractals unique fashionable motifs are created that cannot be found anywhere else!


With us you will find a constantly growing selection of fashionable designs on T-shirts, hoodies, hoodies, polo shirts and baby clothing.


In the universe of chaos and order you will find unusual designs for gifts and accessories.

Discover watercolors, mandalas and creations that look strikingly similar to marine animals, birds or plants and that appear to appear randomly out of the chaos!


Let yourself be surprised and take a look into the fantastic world of images made visible from quantum theory, Heisenberg's uncertainty principle or dynamic systems.


We look forward to your visit, we hope you enjoy the chaos, our designs and products!

Our Team

DARIUS

Physics student


supports with ideas+ programming

DAGMAR

Creative Director


Creative Director of sali-math-arts

FRIEDRICH

Mathematician, Designer


mathematics support for design set up

Contact Us