Image Generator

Instead of simply building and evaluating expressions of integer values as in Arithmetica, you should allow the user to create expressions that evaluate to images. In this program, images are represented as an MxN grid of numeric color values within a specific range (i.e., -1 to 1, 0 to 255, etc.). So, in the simplest sense, this is just building expressions that evaluate grids of numbers instead of a single number.

The result of evaluating an expression in this application is an image. Thus, it will not be practical to print the image to the console after each command. Instead, you should save the result of the expression in a temporary file and use a program (like xv, irfanview, or gimp) to display the results.

Your program should recognize the following expressions:

expression syntax semantics examples

Constant <any real number>
[0-1]+(.[0-9]+)? an image of constant color
87
1.0
0.4

String <any non-quote character between quotes> an image of the given file name is read,
if the image cannot be read, an all black image is produced
"foo.ppm" "images/mickey.ppm"

Variable <any alpha-numeric string>
[a-zA-z0-9]+ an expression represented by a word
a
bugs
q45

Assignment var = expr assigns an expression to a variable
a = 1.0
bugs = "foo/ppm"
a = bugs

Unary Operator op expr prefixes an expression

~ // invert an image

~a
~(t + a * 0.1)

Binary Operator expr op expr combines two expressions into a single expression (in precedence order)

* // times / // divide + // plus - // minus

a + b
a / 2
a + 10 * c

Unary Functions fun(expr) a function that takes an expression as its single argument

sin // sine cos // cosine tan // tangent abs // absolute value

sin(a * b)
abs(x) - y / 2

Multi-Argument Functions fun(expr,...) a function that takes one or more arguments; the first of which is an expression and the second is shown below

color(const, const, const) // image of single rgb color color(string) // image of single "#RRGGBB" color filter(expr, string) // apply kernel from file to expr

color(0.1, 0.5, 1) color("#ff00ff") filter(a, "blur")

Parentheses (expr) raises an expression's precedence
(a + b) * 3
~(bugs - 0.1)

expression	*syntax*	semantics	*examples*
Constant	`<any real number>` `[0-1]+(.[0-9]+)?`	an image of constant color	`87` `1.0` `0.4`
String	`<any non-quote character between quotes>`	an image of the given file name is read, if the image cannot be read, an all black image is produced	`"foo.ppm" "images/mickey.ppm"`
Variable	`<any alpha-numeric string>` `[a-zA-z0-9]+`	an expression represented by a word	`a` `bugs` `q45`
Assignment	`var = expr`	assigns an expression to a variable	`a = 1.0` `bugs = "foo/ppm"` `a = bugs`
Unary Operator	`op expr`	prefixes an expression ~ // invert an image	`~a` `~(t + a * 0.1)`
Binary Operator	`expr op expr`	combines two expressions into a single expression (in precedence order) * // times / // divide + // plus - // minus	`a + b` `a / 2` `a + 10 * c`
Unary Functions	`fun(expr)`	a function that takes an expression as its single argument sin // sine cos // cosine tan // tangent abs // absolute value	`sin(a * b)` `abs(x) - y / 2`
Multi-Argument Functions	`fun(expr,...)`	a function that takes one or more arguments; the first of which is an expression and the second is shown below color(const, const, const) // image of single rgb color color(string) // image of single "#RRGGBB" color filter(expr, string) // apply kernel from file to expr	`color(0.1, 0.5, 1) color("#ff00ff") filter(a, "blur")`
Parentheses	`(expr)`	raises an expression's precedence	`(a + b) * 3` `~(bugs - 0.1)`

Operators have the following precedence from left to right (listed from highest to lowest):

`()`	parentheses
`!`	unary operators
`*`, `/`	multiplicative operators
`+`, `-`	additive operators
`=`	assignment

Extra Credit

Generate images by determining roots of polynomials or iterated fractal systems.

Genetically combine expressions to create more complex expressions.

New Functions

define functions with the following semantics

random()         // create random image expression
mutate(expr)     // create new image from old by introducing random expressions
mate(expr, expr) // create new image from "parents" by randomly combining

Resources

Artificial Evolution for Computer Graphics by Karl Sims (original paper)
Evolver User Guide by Morgan McGuire
Toolkit for Visual Genetic Programming by Tim Rowley

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