# Algorithmic Art

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Summary: We consider ways in which we can use algorithmic techniques to explore design spaces.

Contents:

## Introduction: Algorithmic Grids

Although randomness can provide interesting images and useful programming challenges it is, in the end, a bit too unpredictable for some. Another technique that some artists use to explore design spaces is to break the image up in to a grid and to draw different things in each grid space, with the choice of what to draw based on the position in the grid. For example, we might draw at each location with the same brush, but choose the color for the brush based on the location.

Here's one such strategy for choosing a color:

• Let the red component be 5 times the x coordinate (modulo 256).
• Let the green component be 255 times the absolute value of the sine of the y coordinate. (Since the sine ranges from -1 to 1, multiplying its absolute value by 255 gives us a range from 0 to 255.)
• Let the blue component be the product of the x and the y coordinate (again, modulo 256).

We might define procedures for each of these.

```(define func1
(lambda (x y)
(modulo (* 5 x) 256)))
(define func2
(lambda (x y)
(trunc (* 255 (abs (sin y))))))
(define func3
(lambda (x y)
(modulo (+ x y) 256)))
```

Now, what can we do with these? If you intall `grid.scm` in your GIMP scripts directory (instructions in the lab), you will see that the Script-Fu menu contains a Glimmer submenu with a Color Grid menu item. If you select that meny item, you can choose the size of the grid to build, the spacing between items in the grid, and the procedures for the red, green, and blue components. (Right now, the only valid procedures are `func1`, `func2`, and `func3`, but you can associate any one of the three with each component.)

The Color Grid item does little more than build an image and then recursively step through all the positions in the grid. For each position, it builds a new color (by applying the red procedure to the position, the green procedure to the position, and the blue procedure to the position, and then combining them into a color), and then paints a single dot using the current brush at the position.

For example, suppose we use `func1` for the red component, `func2` for the green component, and `fun3` for the blue component. At the point (10,10), the color gets set to `(50 138 20)`. At the point (50,10), the color gets set to `(250 138 60)`. At that point (200,100), the color gets set to `(232 129 44)`.

## Anonymous Procedures

The color grid technique works well with the three procedures defined above, but clearly there are other ways to convert positions to colors. What should we do if we want a different color component procedure? For example, what if we want the color to depend on the square of the x component?

The most straightforward thing to do is, of course, to (1) create a new procedure (say `func4`) in a file, (2) load the file, and then (3) use that procedure in the dialog. For example, we might write

```(define func4
(lambda (x y)
(modulo (* x x) 256)))
```

However, this is a bit inconvenient. If we just want to try out a new procedure, why do we have have to go back to the editor, type it in, choose a name, go back to the GIMP, load the file, and so on and so forth?

In fact, Scheme programmers often ask a similar question: Why do I have to name this procedure that I'm only going to use once? The answer is, You don't! So, how do we avoid naming these procedures? We might observe that names are just that, names. After the definition `(define grade 95)`, we know that whenever we use `grade`, Scheme plugs in the value `95`. If you wanted to, you could just use `95` rather than `grade`.

It turns out the same thing happens when you define procedures. Whenever you write `func4`, for example, Scheme substitutes `(lambda (x y) (modulo (* x x) 256))`. Then, whenever Scheme tries to apply one of these lambda forms, it does what you'd expect: the Scheme interpreter substitutes the actual parameters for the formal parameters in the body, and then executes the body.

What does this mean to you? It means that you can write the lambda expressions directly. In particular, if we want to try new procedure you can write them in the Red Component, Green Component, or Blue Component fields. For example, we might fill in

• `(lambda (x y) (modulo (+ (* 4 x) (* 3 y)) 256))`
• `(lambda (x y) (modulo (* x y) 256))`
• `(lambda (x y) (modulo (abs (- x y)) 256))`

Since these procedures lack names, we call them anonymous procedures. You will, of course, have the opportunity to try using anonymous procedures in the Color Grid dialog box in the lab.

## Using the Console

As you may recall, one of the reasons that we learned Script-Fu is so that we could enter commands in the console, rather than relying on dialog boxes. Can we draw color grids using the dialog box? Certainly. The `color-grid` procedure accepts seven parameters: the width of the image, the height of the image, the horizontal spacing, the vertical spacing, and the red, green, and blue procedures.

Wait a minute! Those last three parameters sound a bit odd, don't they? Normally, we only pass simple values (numbers, lists, strings, etc.) as parameters. However, in Scheme, you can also pass procedures as parameters to other procedures. For example, we might draw a variant of the original grid image (using `func1` for red, `func2` for green, and `func3` for blue) with the following.

```(color-grid 100 100 12 13  func1 func2 func3)
```

Similarly, we might draw an interesting greyish image with

```(color-grid 100 100 5 5 func2 func2 func2)
```

In fact, we can even use anonymous procedures as parameters here.

```(color-grid 100 100 8 9 (lambda (x y) (modulo (* x y) 256)) (lambda (x y) (modulo (* x 5) 256)) (lambda (x y) (trunc (* 255 (abs (sin (* x y)))))))
```

## Procedures as Parameters, Revisited

We've just seen that you can use procedures as parameters to some procedures. Can you write your own procedures that expect procedures as parameters? Certainly. You treat the procedure as you would any other parameter. For example, here's a procedure that takes a component procedure and draws a grey image using that component procedure for all three components.

```(define grey-image
(lambda (proc)
(color-grid 100 100 5 5 proc proc proc)))
```

We could then draw images with commands like

```(grey-image (lambda (x y) (+ x y)))
(grey-image (lambda (x y) (trunc (abs (* 255 (sin (* x y)))))))
```

But we can do even more. We can apply the procedures that we get as parameters. For example, here's a procedure that takes three component procedures as parameters and sets the color to the color that should occur at (100,100).

```(define standard-color
(lambda (redproc blueproc greenproc)
(set-fgcolor (list (redproc 100 100) (greenproc 100 100) (blueproc 100 100)))))
```

## History

Disclaimer: I usually create these pages on the fly, which means that I rarely proofread them and they may contain bad grammar and incorrect details. It also means that I tend to update them regularly (see the history for more details). Feel free to contact me with any suggestions for changes.

This document was generated by Siteweaver on Thu Sep 13 20:54:59 2007.
The source to the document was last modified on Sun Apr 8 18:21:43 2007.
This document may be found at `http://www.cs.grinnell.edu/~rebelsky/Courses/CS151/2007S/Readings/algorithmic-art.html`.

You may wish to validate this document's HTML ; ; Samuel A. Rebelsky, rebelsky@grinnell.edu

Copyright © 2007 Samuel A. Rebelsky. This work is licensed under a Creative Commons Attribution-NonCommercial 2.5 License. To view a copy of this license, visit `http://creativecommons.org/licenses/by-nc/2.5/` or send a letter to Creative Commons, 543 Howard Street, 5th Floor, San Francisco, California, 94105, USA.