8/8/2019 webMathematica - on the border between Science and Art by Dr Monika Kovacova, Slovak Technical University (Slovakia):
1/38
Vine and Table cloth - two geometries.
8/8/2019 webMathematica - on the border between Science and Art by Dr Monika Kovacova, Slovak Technical University (Slovakia):
2/38
The project SCIENAR explicitly aims in particular
to create an interactive environment for both Scientist and
Artists,
through this environment Scientists can explore the role that
Mathematics plays in understanding and making Art, as well
as produce mathematical objects that are useful in Art; while Artists can found mathematical structures and forms
that they can directly use, without needing the subtleties of
Mathematics, to inspire and produce their artworks.
ONE OF POSSIBLE WAYHOW TO FILL UP THIS AIM IS
webMATHEMATICA
8/8/2019 webMathematica - on the border between Science and Art by Dr Monika Kovacova, Slovak Technical University (Slovakia):
3/38
We will speak in this speech
1. about webMathematica as a possible tools for
producing artistic objects
2. about Lindenmayer systems, fractal plants and
Random walking as one of possible concepts
3. about our result achieved by the interaction between
science and art sphere in Slovakia
4. about the possibility - how to use dynamical webpages in creating Your own "piece of art"
8/8/2019 webMathematica - on the border between Science and Art by Dr Monika Kovacova, Slovak Technical University (Slovakia):
4/38
What is webMathematica?
WEBMATHEMATICA ENABLES THE CREATION
OF DYNAMICAL WEB SITES
THAT ALLOW USERS TO COMPUTE AND VISUALIZE
RESULTS DIRECTLY FROM A WEB BROWSER.
All of the computational power in Mathematica is available to
build special calculators and problem solvers that are
delivered over the web or over your corporate intranet to the
specific intranet site.
The development process is so simple that mostMathematica users can proceed through it without having
to go through long development cycles or needing the
services of dedicated developers.
In many cases, all that is required is adding the Mathematica
commands and a couple of simple tags to a web page.
8/8/2019 webMathematica - on the border between Science and Art by Dr Monika Kovacova, Slovak Technical University (Slovakia):
5/38
What is webMathematica?
webMathematica technology
The web interaction of webMathematica is provided by a Java
web technology called Java servlets. Servlets are special Java
programs that run on a web server machine.
Support is provided by a separate program called a servlet
container(or sometimes a "servlet engine") that connects to theweb server. One of popular servlet container is Apache Tomcat.
Essentially all modern web servers support servlets natively
or through a plug-in servlet container.
Closely related to Java servlets are Java Server Pages (JSPs);
both servlets and JSPs integrate very closely with
webMathematica.
The computation and visualization engine for
webMathematica is Mathematica.
8/8/2019 webMathematica - on the border between Science and Art by Dr Monika Kovacova, Slovak Technical University (Slovakia):
6/38
What is webMathematica?
webMathematica technology
And now for artists - simple and more useful
webMATHEMATICA allows a site to deliver HTML pages
that are enhanced by the addition ofMathematica
commands.
When a request is made for one of these pages, the
Mathematica commands are evaluated and the computed
result is inserted into the page and delivered to the client
browser.
8/8/2019 webMathematica - on the border between Science and Art by Dr Monika Kovacova, Slovak Technical University (Slovakia):
7/38
What is webMathematica?
webMathematica technology
And now for artists - simple and more useful
How it works ?
1. Browsersent requests to webMathematica server.
2. webMathematica serveracquire Mathematica kernelfrom the
pool.
3. Mathematica kernel is initialized with input parameters, it
carries out calculations, hand returns result to server.
4. webMathematica serverreturns Mathematica kernelto the
pool.
5. webMathematica server returns result to browser.
8/8/2019 webMathematica - on the border between Science and Art by Dr Monika Kovacova, Slovak Technical University (Slovakia):
8/38
What is webMathematica?
webMathematica technology
We can demonstrate the real applicationrunningon one part of Lindenmayer turtle graphics.
8/8/2019 webMathematica - on the border between Science and Art by Dr Monika Kovacova, Slovak Technical University (Slovakia):
9/38
What is webMathematica?
webMathematica technology
1st step
Browser sends request to webMathematica server.
You can write to the web browser YOUR own Axiom,
Replacement rules, Number of iterations and Angle of
rotation.
How to choose these parameters is explained on all
created webMathematica pages.
How it works in real ?
explanation for artistson example of Lindenmayer systems
8/8/2019 webMathematica - on the border between Science and Art by Dr Monika Kovacova, Slovak Technical University (Slovakia):
10/38
What is webMathematica?
webMathematica technology
2nd step
webMathematica server acquires Mathematica kernel from the
pool.
Don't understand? Never mind!
This server activity is realized automatically, withoutany needs from user.
Fractals - Lindenmayer Systems
How it works in real ?
explanation for artistson example of Lindenmayer systems
8/8/2019 webMathematica - on the border between Science and Art by Dr Monika Kovacova, Slovak Technical University (Slovakia):
11/38
What is webMathematica?
webMathematica technology
3rd step
Mathematica kernel is
initialized with input
parameters, it carries outcalculations, hand returns
result to server.
Don't understand? Nevermind!
This server activity is realized
automatically, without any
needs from user.
LSystemWithF[axiom_, (* initial sequence *)
rules_, (* replacement rules *)
iterations_, (* number of iterations *)\[Delta]_ (* angle of rotation *)] :=
Module[{minus, plus, fastRules, last, direction},
(* computation of the two rotation matrices, for "right" and "left" *)
minus = {{ Cos[ \[Delta]], Sin[ \[Delta]]}, {-Sin[ \[Delta]], Cos[ \[Delta]]}};plus = {{ Cos[-\[Delta]], Sin[-\[Delta]]}, {-Sin[-\[Delta]], Cos[-\[Delta]]}};
(* we rewrite the replacement rules in a form that is faster.*)fastRules = rules /. {(a_ -> b_) -> (a :> Sequence @@ b)};
(* Initial position and direction *)
last = {0, 0}; direction = {1, 0};
(* - multiple application of the replacement rules using Nest- interpretation of F, + and - using Which.
If "only" the direction direction is to be altered, the result is ...; , i.e.,
Null- add the initial position using Prepend
- sort out all "non - motions" - i.e. Null using Select *)
Select[Prepend[(Which[# == "F", last = last + direction,# == "+", direction = plus.direction;,
# == "-", direction = minus.direction;]& /@Nest[(# /. fastRules)&, axiom, iterations]),
{0, 0}], (* select all points *) # =!= Null&]]
How it works in real ?
explanation for artistson example of Lindenmayer systems
8/8/2019 webMathematica - on the border between Science and Art by Dr Monika Kovacova, Slovak Technical University (Slovakia):
12/38
What is webMathematica?
webMathematica technology
4rd step
webMathematica server returns Mathematica
kernel to the pool.
Don't understand? Never mind!
This server activity is realized
automatically, without any needs
from user.
How it works in real ?
explanation for artistson example of Lindenmayer systems
8/8/2019 webMathematica - on the border between Science and Art by Dr Monika Kovacova, Slovak Technical University (Slovakia):
13/38
What is webMathematica?
webMathematica technology
How it works in real ?
explanation for artistson example of Lindenmayer systems
5th step
webMathematica server returns result to browser.
Do you want see it in practice?
Look at ...
http://www.webmathematica.eu/Scienar1/index.php
8/8/2019 webMathematica - on the border between Science and Art by Dr Monika Kovacova, Slovak Technical University (Slovakia):
14/38
What is webMathematica?
webMathematica technology
How it looks ?
real webMathematica pages
8/8/2019 webMathematica - on the border between Science and Art by Dr Monika Kovacova, Slovak Technical University (Slovakia):
15/38
What is webMathematica?
webMathematica technology
Do you want see it in practice?
Look at ...
http://www.webmathematica.eu/Scienar1/index.php
8/8/2019 webMathematica - on the border between Science and Art by Dr Monika Kovacova, Slovak Technical University (Slovakia):
16/38
Lindenmayer systems
Mathematics and beauty plants
Fractal geometry is appropriate for many natural forms.
Natural shapes which are well-approximated by fractals
include clouds, mountains, trees, bushes, rocks, dirt,
leaves, snow flakes, lightning, turbulent water, tree bark,rugged coastlines, brain convolutions, capillary beds,
bronchial tubes, and the distribution of galactic clusters.
To the artist, well-approximated means visually
convincing, while to the scientist it means descriptiveand/or predictive in a quantitatively meaningful way.
8/8/2019 webMathematica - on the border between Science and Art by Dr Monika Kovacova, Slovak Technical University (Slovakia):
17/38
The beauty of plants has attractedthe attention of mathematicians for centuries.
Geometric features such as the bilateral symmetry of leaves, the
rotational symmetry of flowers, and the helical arrangements of
scales in pine cones have been studied most extensively.
Beauty is bound up with symmetry.
In case we want to understand the beauty of flowers from the
mathematical point of view, it is need to analyze two separate
look in for that prolem.
The first is the elegance and relative simplicity
ofdevelopmental algorithms.
The second is self-similarity.When each piece of a shape is
geometrically similar to the whole, both the shape and the cascade
that generate it are called self-similar.
Lindenmayer systems
Mathematics and beauty plants
8/8/2019 webMathematica - on the border between Science and Art by Dr Monika Kovacova, Slovak Technical University (Slovakia):
18/38
Thus, self-similarity in plants is
a result of developmental processes.
The developmental processes are captured using theformalism ofmodeling of L-systems.
L-systems were introduced in 1968 by Lindenmayer as a
plants theoretical framework for studying the development of
simple multi-cellular organisms.
After then the plant models expressed using L-systems
became detailed enough to allow the use of computer graphics
for realistic visualization formal graphics languages but also for
visualization of plant structures and developmental processes.
Lindenmayer systems
Mathematics and beauty plants
8/8/2019 webMathematica - on the border between Science and Art by Dr Monika Kovacova, Slovak Technical University (Slovakia):
19/38
In 1968 a biologist, Aristid Lindenmayer, introduced a new
type ofstring-rewriting mechanism,
subsequently termed L-systems.
L-systems are applied in parallel and simultaneouslyreplace all letters in a given word.
The generated structures are one-dimensional chains of
rectangles, reflecting the sequence of symbols in the
corresponding strings.
In order to model higher plants, a more sophisticated
graphical interpretation of L-systems is needed
we will show it later.
Lindenmayer systems
Mathematics and beauty plants
8/8/2019 webMathematica - on the border between Science and Art by Dr Monika Kovacova, Slovak Technical University (Slovakia):
20/38
Lindenmayer systems
Mathematics and beauty plants
8/8/2019 webMathematica - on the border between Science and Art by Dr Monika Kovacova, Slovak Technical University (Slovakia):
21/38
Lindenmayer systems
Mathematics and beauty plants
How it looks ?webMathematica pages - in real
8/8/2019 webMathematica - on the border between Science and Art by Dr Monika Kovacova, Slovak Technical University (Slovakia):
22/38
Lindenmayer systems
Mathematics and beauty plants
"axiom " F - F - F - F
"replacement rule " F F F - F + F - F - FF
"axiom " F - F - F - F
"replacement rule " F F - F F - - F - F
8/8/2019 webMathematica - on the border between Science and Art by Dr Monika Kovacova, Slovak Technical University (Slovakia):
23/38
Lindenmayer systems
Mathematics and beauty plants
webMathematica pages - in realWe can create also automatic generator for L-systems.
It can produce also very attractive results.
8/8/2019 webMathematica - on the border between Science and Art by Dr Monika Kovacova, Slovak Technical University (Slovakia):
24/38
Lindenmayer systems
Mathematics and beauty plants
8/8/2019 webMathematica - on the border between Science and Art by Dr Monika Kovacova, Slovak Technical University (Slovakia):
25/38
Lindenmayer systems
Mathematics and beauty plants
Here are results produced by turtle walking (Lindenmayer systems)See also (gallery or create Your own)
http://www.webmathematica.eu/Scienar1/index.php/l-systems
8/8/2019 webMathematica - on the border between Science and Art by Dr Monika Kovacova, Slovak Technical University (Slovakia):
26/38
Lindenmayer systems
Mathematics and beauty plants
Here are results produced by turtle walking (Lindenmayer systems)See also (gallery or create Your own)
http://www.webmathematica.eu/Scienar1/index.php/l-systems
8/8/2019 webMathematica - on the border between Science and Art by Dr Monika Kovacova, Slovak Technical University (Slovakia):
27/38
Lindenmayer systems
Mathematics and beauty plants
8/8/2019 webMathematica - on the border between Science and Art by Dr Monika Kovacova, Slovak Technical University (Slovakia):
28/38
Lindenmayer systems
Mathematics and beauty plants
According to the rules presented before, the turtle interprets
a character string as a sequence of line segments.
Depending on the segment lengths and the angles between
them, the resulting line is self-intersecting or not, can be more
or less convoluted, and may have some segments drawn many
times and others made invisible, but it always remains just a
single line.
However, the plant kingdom is dominated by branching
structures; thus a mathematical description of tree-like
shapes and methods for generating them are needed formodeling purposes.
An axial tree complements the graph-theoretic notion of
a rooted tree with the botanically motivated notion of branch
axis.
8/8/2019 webMathematica - on the border between Science and Art by Dr Monika Kovacova, Slovak Technical University (Slovakia):
29/38
Lindenmayer systems
Mathematics and beauty plants
Root or base
In the biological
context, these
edges are referred
to as branch
segments.
Internode
A terminal
segment (with no
succeeding edges)
is called an apex
Plants are generally modeled with a special type of rooted
tree called an axial tree.
8/8/2019 webMathematica - on the border between Science and Art by Dr Monika Kovacova, Slovak Technical University (Slovakia):
30/38
Lindenmayer systems
Mathematics and beauty plants
Bracketed string representation
of an axial tree
F[+F][-F][-F]F]F[+F][-F]
Here are results produced by Fractal Plants application
See also (gallery or create Your own plants on)
http://www.webmathematica.eu/Scienar1/index.php/l-systems
8/8/2019 webMathematica - on the border between Science and Art by Dr Monika Kovacova, Slovak Technical University (Slovakia):
31/38
You can
create
Your own
plant
simple,
safety
and Your
plants do
not want
water for
long time.
http://www.webmathematica.eu/Scienar1/index.php/l-systems/
webmathematica/157-lindenmayers-plants
8/8/2019 webMathematica - on the border between Science and Art by Dr Monika Kovacova, Slovak Technical University (Slovakia):
32/38
Lindenmayer systems
Mathematics and beauty plants
"axiom " X
"replacement rules " X F X + X + F + F X - X " "
" " F F F" "
"axiom " X
"replacement rules " X F X + X + F + F X - X - X + F + FX " "
" " F F F" "
8/8/2019 webMathematica - on the border between Science and Art by Dr Monika Kovacova, Slovak Technical University (Slovakia):
33/38
Lindenmayer systems
Mathematics and beauty plants
And the real art application?
The following application were created by Slovak
students of School of Applied Art,
cat Birch tree
8/8/2019 webMathematica - on the border between Science and Art by Dr Monika Kovacova, Slovak Technical University (Slovakia):
34/38
cat Birch tree
Lindenmayer systems
Mathematics and beauty plants
8/8/2019 webMathematica - on the border between Science and Art by Dr Monika Kovacova, Slovak Technical University (Slovakia):
35/38
Other applications
Starting with such an image, and creating mirror images to
the left, below, and lower left, we get an image that is typical
for a kaleidoscope.
Art application inspired by
webMathematica application
8/8/2019 webMathematica - on the border between Science and Art by Dr Monika Kovacova, Slovak Technical University (Slovakia):
36/38
Other applications
We take a curve given in the form list
of circles and their parts and reflect
parts of this curve on some randomly
selected segments list of points.
8/8/2019 webMathematica - on the border between Science and Art by Dr Monika Kovacova, Slovak Technical University (Slovakia):
37/38
Other applications Penrose tilling
8/8/2019 webMathematica - on the border between Science and Art by Dr Monika Kovacova, Slovak Technical University (Slovakia):
38/38
Other applications
Thank You very much and
You are welcome onYou are welcome on
http://www.webmathematica.eu/Scienar1/index.php
Altering server
http://www.webmathematica.eu/Scienar/index.php
Top Related