Design Statement
        In order to create a procedure which generates at least one thousand distinct images from a given number, n, (as well as desired width and height) that number must have an effect on several various characteristics of the image.  I intend to create a procedure that achieves variation in method of drawing, fundamental shapes and patterns, color scheme and values.  The various drawings that result from the procedure exhibit several known techniques for drawing, varied over different shapes and patterns, varied over different color tones and schemes, drawn in varying types of brushes.
        Though so much variation at first glance appears chaotic, bordering on random, the mathematics behind the procedure allows for interesting yet absolutely predictable behavior.  For example, the resulting images from integers with a difference of 210 will all be essentially the same, but iterated in different color schemes.  All characteristics of the drawing, in fact, can be deduced through trial and error, ultimately by knowing the prime factor(s) of n.
        The color schemes will be based on the fundamentals of design and color; whether monochromatic, analogous or complementary, warm or cool, all resulting images will achieve harmony since their components will always be determined relative to one another.  The form(s) drawn will not necessarily be symmetrical, but will each certainly be balanced within the greater composition.
        This project is a study in visual and numeric harmony, both displayed through image rendering.  While anyone can generate colorful, interesting images with this procedure by trying out various values of n, those with a mathematical brain can try testing their knowledge of factors and enjoying the results either way.


Technique Statement
        To achieve this minimum of one thousand distinct images, with only one integer to manipulate, I need to ensure that there is enough variation in the method of drawing, basic shapes and patterns, color schemes and values.  First I will split the natural numbers 0-999 into five groups of 200 (0-199, 200-399, etc) which will each have a different type of color scheme (monotone with varied value, warm complementary, cold analogous, cold complementary, warm analogous).
There will be four further levels of variation achieved using modulo: every other integer will have the background set to the darker color available and vice versa; the fundamental shapes used will vary between circle, square, and other polygons; the method of drawing used will vary between GIMP tools, simple algorithms, pixel-based computations, turtle graphics, and fractal recursion; finally, there will be a selection of seven interesting, distinct brushes that do not obscure the shapes produced, even at small sizes.
        Since I have involved four levels of variation over all relatively prime numbers, they allow for 2 * 3 * 5 * 7 = 210 unique possibilities; combined with the five various color schemes, grouped consecutively rather than using modulo, there are a total of 210 * 5 = 1,050 possible unique images.  For each method of drawing used, the given width and height will correlate to the size of the resulting image, and the drawing within will also be scaled down to that size; that is, given the same integer with doubled width and height, the same image should simply appear enlarged but otherwise unchanged.
        I have two main concerns that may need to be addressed as I implement this procedure.  One is the “cost” of the procedure, as in how long it will take to run, especially given the several tests which must be made before determining anything about the drawing.  The other is a more abstract, stylistic question of cohesion and visual harmony: since there will so much variation between the resulting images, I fear it will not be much of an image series as much as a set of predictable but unrelated images.


112, 257, and 453 all produce images that are particularly interesting to me.  The first, with modn3 = 1 and modn5 = 2 is a rectangular, turtle-based operation.  The second with modn3 = modn5 = 2 is a polygonal, also turtle-based operation.  The last is an image created with an algorithm, and based upon an ellipse.  These three examples highlight the magnitude of variance allowed for in this procedure.  (The last example unfortunately pops up with an entirely new canvas, separate from the one that image-series originally generates).