Graphica 2

Artistic Rendition of Data for Fun &
 Profit

Igor Bakshee 

Wolfram Research, Inc.

Philosophy :  What Makes an Attractive Image?

Strong a Claim 1

Strong a Claim 2

A human relates him/her-self to a visual image if the eye catches 
traces of regularity.

Conjecture

Marketing Claim 1

Marketing Claim 2

Starting from June 18, 1998 (the day the Worldwide Mathematica Conference opened), Artlandia is available on the WWW as a commercial product (http://www.artlandia.com/).

Disclaimer

WRI should not be held responsible for any drawbacks in the software, 
since Artlandia is my hobby project.

I do wish to take this opportunity, though, and thank WRI for its 
encouraging interest to the project from its inception and gracious marketing 
support and I hope we will soon be distributing Artlandia together.

Applications :  

          Who needs artificially generated images anyway?

Who said "Artificially"?

Sources may and do come from natural sources—experimental or 
simulated data or algorithms—say, mountain relief.

Or heart beat data.

Or music.

See below re kinds of processes.

In fact, data may be arbitrary (example: graphical interpretation of the words "scientific data 
management"—an artwork that appeared on the cover of magazine http://www.artlandia.com/covers/SDM).

Market (for the designs in the narrow sense)

It turns out that, even barring the imaginary applications, there already 
exists a market for "artificial" designs in textiles, wallpaper, carpeting, 
gift wrap, etc...

In fact, we've built a small business around such designs, Artlandia, Inc.
—and a very positive acceptance of Artlandia designs by the market has encouraged us to further develop our graphic 
techniques into a marketable software product and bring Artlandia to the market.

People create as they live ...

Generating graphics with a mathematical tool is as good a hobby as 
painting... and we've decided to price the first version of Artlandia so that it'll be within an easy reach for hobbyists... although Artlandia is a professional tool.

Basic Steps

Types of random processes

Basic Types of Random Processes

<< Artlandia`

ListPlot[RandomArray[200], PlotJoined -> True];

ListPlot[NaturalArray[200], PlotJoined -> True];

ListPlot[RandomWalkArray[200], PlotJoined -> True];

2  D Incarnations

raster[array_]  :=  

      Show[Graphics[Raster[array, ColorFunction -> Hue]], 

        AspectRatio -> Automatic];

raster[RandomArray[{100, 100}, {0, 1}]];

raster[NaturalArray[{100, 100}, {0, 1}]];

raster[RandomWalkArray[{100, 100}, {0, 1}]];

Generating Arbitrary (Not Necessarily Numerical) Arrays

ArrayOf[{a, b},  {10, 10}]

ArrayOf[{a, b},  {10, 10}, GeneratingFunction -> RandomArray]

ColorBar[Shades[(({{Red, Yellow}, {Blue, Green}, {Banana, Violet}})),40],OrderingFunction -> None];

ColorBar[Shades[(({{Red, Yellow}, {Blue, Green}, {Banana, Violet}})),40,GeneratingFunction -> Ramp],OrderingFunction -> None];

"Natural" Truchets

As a more practical illustration we consider random Truchet patterns, those based on the Sebastien Truchet's tiling (see, e.g., E.H. Gombrich, The Sense of Order. Cornell University Press, Ithaca, New York: 1979). We will define a 
Truchet function that creates two types of tiles, each formed by a pair of 
quarter circles. Depending on the value of the first argument, which can be 
either 0 or 1, the centers of the arcs are arranged either top left and lower 
right, or top right and lower left. (Mathematica implementation after Paul Abbott.)

Truchet[0, {x_, y_}] := {

        Circle[{x, y + 1}, (1/2), {-(π/2), 0}], 

        Circle[{x + 1, y}, (1/2), {(π/2), π}]}

Truchet[1, {x_, y_}] := {Circle[{x, y}, (1/2), {0, (π/2)}], 

        Circle[{x + 1, y + 1}, (1/2), {π, ((3 π)/2)}]}

Show[

      GraphicsArray[

        Graphics[Truchet[#, {0, 0}], AspectRatio -> 1]&/@{0, 1}], 

      GraphicsSpacing ->  .1];

TruchetMatrix[mat_] := MapIndexed[Truchet, mat, {2}]

Show[

          Graphics[

            TruchetMatrix[

              ArrayOf[{0, 1}, {30, 30}, GeneratingFunction -> #]], 

            AspectRatio -> Automatic]]&/@{RandomArray, NaturalArray, 

        RandomWalkArray};

Several similar "natural" mazes of different periods, one overlaid on 
the other, lead to a beautiful lace image that appears in Graphica 2. Here is 
the algorithm to generate a simplified lace that consists of n = 12 tilings. Artlandia users can reproduce the larger image in the book with n = 30.

n = 30;

The color palette for the pattern consists of a spectrum of n shades from 
RGBColor[.8,1,1] (a very light blue) to the white color. Note that, by 
default, the Shades function automatically creates the natural distribution 
of colors in the given color range.

colors = Shades[{RGBColor[ .8, 1, 1], White}, n];

Here is the superposition of  n  tilings of different scales combined in one 
image; the coarser tilings are drawn with thicker lines.

\(\(Show[

      CombineGraphics[

        MapThread[

          Graphics[{AbsoluteThickness[10. \/#], #2, 

                TruchetMatrix[ArrayOf[{0, 1}, {#, #}]]}, 

              AspectRatio -> 1, PlotRange -> All]&, {

            Round[NaturalArray[n, {5, 20}\ \ ]], colors}], 

        Background -> CornflowerBlue, ToSameSize -> Automatic], 

      AspectRatio -> 1]; \)\)

Also in Artlandia

http://www.artlandia.com/software/toc.html

Kaleidoscope:  Design with a click of the mouse

http://www.artlandia.com/kaleidoscope

In Conclusion

We have developed a Mathematica application that facilitates easy conversion of data into artistic images
—the process illustrated the Graphica 2 book. The tools have been 
created to operate on layers of graphics objects as well as on individual 
primitives. Common operations are automated, such as adding a 
"controllable" randomness, spreading numerical arrays along and across 
lines or on the plane, color coordination, etc. Geometric utilities, such as 
creating wallpaper patterns from an arbitrary graphics are in the package, 
too.

With Artlandia, you can now create by thinking on the level of image primitives, without 
boggling down in the chores of implementation.

Drum Roll... Winners of the First Artlandia Kaleidoscope Contest!

http://www.artlandia.com/contest/