### Forward--Into The Past

For my first foray into the world of Artlandia, I thought I'd experiment with some early algorithmic art made by a former professor/adviser and eventual colleague of mine, Bill Kolomyjec. The bulk of his early work during the early 1970's was done at Michigan State University using BASIC programs on a then state-of-the-art PDP-11 connected to a plotter. Here's one of my favorite pieces, Boxes I.

Boxes I - Bill Kolomyjec, 1973

The nucleus of this work is a grid system, making it a good candidate for experimentation with Artlandia. The following code shows the simple lattice from which Boxes I was created. The Artlandia function` Tile `contains a set of graphics primitives and a tiling group that tells Artlandia how the graphics primitives are arranged into wallpaper patterns. In this example we are using a tiling group, which is essentially a rectangular grid system. The `Tiling `command creates a set of graphics primitives that can be rendered with `Show`.

In that particular work each square is rotated and translated by an amount proportional to its distance from the edge of the grid. Conveniently, Artlandia contains a full set of geometry manipulation utilities. Here we create a function for manipulating the square, `BoogieWoogie`, that uses the `Rotate` and `Translate` functions to randomly displace the graphics primitives by some amount.

This snippet of programming calculates scaled city-block distances from the edges of the lattice on the interval [0,1]. The resulting distance is scaled by an adjustable exponential falloff to make the effect more pronounced or limited.

Putting it all together, we can create a matrix of tiles, each tile displaced and rotated by an amount proportional to its city-block distance from the edge of the figure.

Voila! Crank up your plotter and take a giant step back into the world of '70s computer art.

One nice feature of Artlandia is that there is more than one way to do most anything (as is traditional with Mathematica).  Some designs lend themselves more readily to methods other than that used above. For example, the `Lattice` command could have been used to create the grid and a tile could have been constructed and drawn at each point in it, rather than depending on `Tiling`. However, `Tiling` allows us to experiment with more variations on Kolomyjec's theme.

Converted by Mathematica      September 24, 1999

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