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Summary: We consider ways in which we can use algorithmic
techniques to explore design spaces.
Contents:
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
menu contains a
submenu with a 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).
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.
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)))))))
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)))))
;
