Artlandia :  
        Turning Mathematica into a Graphic Design Machine

Igor Bakshee

Wolfram Research, Inc., and Artlandia, Inc.

Teaching Mathematica to make interesting patterns, ornaments, wallpaper images, and other types of decorative compositions and algorithmic art is easy with Artlandia, the first Mathematica application for creative graphic design. The demonstration shows how Artlandia, now in Version 1.5, brings the design process within the reach of a student or hobbyist. Artlandia further suggests a stream of plausible solutions and makes you magnificently productive in your design work.

Step 1: Use Computer to Create Forms and Paints Them for You

The main distinguishing feature: complete programmatic control.

<< Artlandia`

Artlandia: A visual tool

Example: it is simple to make a comb (using the built-in functions).

alternate[list_]  :=  
      Flatten[{0,  Transpose[{list, Table[0, {Length[list]}]}]}]; 
ListPlot[alternate[Range[12]], PlotJoined -> True];

Artlandia's function Crown allows you to build such comb along an arbitrary curve.

line  =  Line[Ellipse[1. , {0, π}] // Reverse]; 
Show[Graphics[line]];

Show[
      Graphics[{{Red, Line[Crown[alternate[Range[12]/20], line]]}, line}]];

Dozens of geometric tools, transformations, operations on primitives and layers, combinations...

Including non-traditional ones like MatchConnect⟶ which the engine that creates some Graphica 2 images example.

Performs Traditional Graphics Operations

SeedRandom[1]; 
poly  =  Polygon[RandomArray[{10, 2}]];

Show[Graphics[{Red, poly}]];

tile  = 
      Tile[{Red, poly}, 𝓅3𝓂1, Boundary -> Automatic, 
        ControlPoints -> {{- .2, - .2}, { .2,  .2}}]

Show[UnitCellSchematic[tile], Graphics[tile]];

Show[Tiling[tile, {4, 5}]];

Creates Color Palettes (and Paints)

ColorBar[Shades[{Red, Yellow}, 40, GeneratingFunction -> Ramp]];

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

Step 2: Use the Magic Wand

Touch of Randomness transforms a static image into a live one: of MiER.

Also magically increases productivity.

Who Needs That Noise?

http://www.graphica.com/applications

Some Recent Designs

More Designs

Artlandia gallery.

Further Reading

Graphica 2: The Pattern of Beauty: http://www.graphica.com.

Flip Phillips,  Artlandia: Cool tools for algorithmic aesthetics. The Mathematica Journal, 1999, No. 3.

Bakshee, Igor, 1998, Exploring Artlandia. Mathematica in Education and Research, v. 7, no. 4, pp. 46-55.

Peterson, Ivars, 1998. MathTrek: Visiting Artlandia. Science News Online.

Summary