Design Statement
	 Each image in my series is made up of 16 polygons layered upon a background.  The series is composed of over 1000 distinct images which vary by type of polygon used, rotation difference between successive polygons, center of individual polygons, and color scheme.  I began this design with the intention of using polygons to explore depth.  After completing the design I found that the variation between images was better suited toward the exploration of dimension, including but not limited to depth.
	 The base polygon of each image has a side-length equal to the image width and is centered on the top left third of the image.  15 additional polygons are superimposed upon the base polygon, with each polygon being 90% the size of the previous.  The fill of each successive polygon increases in value, creating a tinted gradient between the base and top polygons.  Color of the base polygon is may be one of 10 colors and is determined by the last digit of n.  Since this single color is applied every polygon in varying degrees of lightness, the color schemes of all images in the series are monochromatic.  Polygons are outlined in successively lower values of their corresponding color for values of n greater than 999, creating a shade.
	 Assuming that n is a four-digit or lesser-digit number prepended by zeroes, the polygon contained within any given image of the series is determined by the second digit of n.  When numbers 0 through 4 are contained as the second digit, the polygon created has 3 sides more than this number.  For example, the number 1011 will produce an image containing triangles.  Each of these polygons is centered on the top left third of the image.  When numbers 5 through 9 are contained as the second digit, the polygon created has 3 sides more than the remainder of this number divided by 5.  For example, the number 1711 will produce an image containing squares.  The base polygon for these numbers is centered on the top left third of the image while each successive polygon is centered at coordinates that are 95% of its predecessor.  All images of the series are asymmetrical, with visual weight gravitating toward the top, left corner of the image.
	 Amount of rotation between polygons is dependent upon the third digit of n.  Values of n containing 0 in this position display no rotation between polygons.  Values of n containing 1 in this position display a 10% amount of rotation between polygons, relative to the amount the polygon would have to rotate to superimpose upon itself.  Values of n containing 2 in this position rotate 20%, values containing 3 rotate 30%, and so on.  The base polygon is always be oriented so that the horizontal line crossing its center will bisect an interior angle on the right half of the polygon.
	 My original plan for the image series was to use only heptagons and to vary images by changing the number of heptagons present.  While this did lead to a few visually interesting pictures, I found it more interesting as a series to leave the number of polygons present within each image constant and instead vary the type of polygon used.  Although this quantitatively led to the same number of distinct images, I found that it benefitted the design by creating more purposeful variation between images, leaving each image uniquely different rather than very close to the same.  Another change I found necessary in implementing the design was from the use of outlined to filled or filled and outlined polygons, which better visualized the color change between polygons.
	From viewing various images of this series it appears that overlapping and rotating polygons whose colors change along a monochromatic gradient creates the appearance of elevation, or layers.  When polygons of this gradient are overlapped but not rotated, the resulting image can be seen either as having depth or elevation.  It would be interesting to adapt this series further in order to explore whether the use of a dichromatic gradient or no gradient would create the same illusion of dimension.
 
Technique Statement
	 I know that all values of n for 0 <= n <= 999 create distinct images because each digit of n corresponds to a specific type of variation within the image and each digit creates 1 of 10 possible instances of its variation.  
	Assuming that n is a four-digit number, the second digit determines the number of sides the polygons will have and whether or not the center will be shifted (explained in more detail below). An image will contain polygons with anywhere from 3to 7 sides and polygons either will or won’t share a common center; 10 instances of variation corresponding to side-number and center can be created based on the second digit of n. 
	 The third digit of n corresponds to the amount of rotation between successive polygons, which is equal to 0.1 * (the number in the second digit of n) * (the angle the polygon must rotate to superimpose upon itself).  The amount of rotation is a fraction of the amount required for the polygon to superimpose upon itself. This ensures that the same image is not created twice and that the third digit of n can create 10 distinct instances of rotational variation.  
	 The fourth digit of n corresponds to the initial polygon color.  The color is referenced, based on the fourth digit of n, from a list of 10 different colors.  
	 Since each of these 3 digits of n is corresponds to a different type of variation and since each digit is able to create 10 different instances of its variation, 10 * 10 * 10 combinations of these variations are possible, and 1000 distinct images can be made.  In addition, for values of n greater than 999 the polygons are outlined, doubling the total number of distinct images that can be made to 2000.
	The most important algorithm used in my design is recursion.  One procedure, make-polygon!, is called multiple times in any given image of the series.  Recursion is essential to the design because it is what allows for the variation between polygons; color, side-length, orientation, and center of the polygon are changed through numeric recursion.  The parent procedure image-series sets the recursive procedure to create a fixed number of polygons for any image.  image-series sets fixed ratios to create changes in polygon side-length and center, while the recursive procedure itself sets the color transforms to be applied to each polygon.  The orientation of each polygon is determined by n.  These 4 changes are implemented through the use of recursion, creating variation within each image.
	 Another important algorithm used in this design is the creation of new lists from the combination and manipulation of existing lists.  Two lists are created by mapping, to a list of angles, procedures that calculate x- and y-coordinates based on angles.  These lists are used to store the polygon’s x- and y-coordinates, which are then combined into a new list using merge-list, which is then used to create yet another list using merge.  Creating new lists through a series of steps is a useful algorithmic technique in this case because it allows the procedure to calculate individual x- and y-coordinates separately from one another and then arrange them in a list of alternating order, as is necessary to use in image-select-polygon!.  The creation of these lists relies on recursion, which is important in building the list of alternating x- and y-coordinates.  Another important algorithm in my procedure is list-ref, which allows the computer to find and retrieve values stored in a list. list-ref is used to determine polygon color in my image series.
	 Conditionals are a final algorithm used in creating this image series.  I found that after many increases in number of polygon sides the images start to become less interesting.  Instead of increasing the number of polygon sides based on every value of the second digit of n (assuming n is a four-digit number) I decided to increase the number of sides based on the remainder of the second digit of n when divided by 5.  Doing this causes the images to repeat for values of n whose second digit is greater than 4.  Because of this, I used an if-statement to check whether the second digit was greater than 4; for values less than four I decided to keep every successive polygon centered at 0 and for values greater than four I decided to shift the polygon center up and left by a ratio of 0.95.  By using an if-statement I was able to limit variation in one way and create it in another, ensuring that all values of n create distinct images.

Values to Use for n
	34, 159, and 335 create particularly interesting images when used as n.