Design Statement 

	In this project, I intend to create a geometric design centered on a central point.  The basic design is that of a Fibonacci spiral beginning from a central point.  A Fibonacci spiral contains many quarter-circles adjoined to each other, each of which has a radius of the next Fibonacci number, increasing outwardly. However, in addition to the usual basic circular line of the spiral, some spirals will use curved fractal lines as it spirals out from the center.  This design will be replicated and rotated three times ninety degrees from the original, then overlaid onto four basic fibonacci spirals oriented in the same way, so that there are eight overlaying spirals.  I intend to create a ground (negative space), in the shape of a circle, that contains the entire spiral, whose color is the complement of the color of the spiral.  This ground will be a darker version of the color of the spiral, emphasizing the spiral design.  I intend for the final image to be monochromatic, only containing shades of a specific color, in order to emphasize the geometrical curves of the shape.  The image will be scaled in such a way that the maximum of the spiral width and height should align nearly perfectly with the minimum of the image's width and height.  The circle's width equals the drawing's width, and the circle's height equals the drawing's height.

Technique Statement

	This project will use recursion, drawings, the modulus function, turtles, and fractal concepts.  The color of the spiral is determined based upon the input parameter, n.  The color, degree of the fractals, and radii of the spirals will be dependent upon the inputs, creating over 1,000 distinct images. The ratio of the radii of the circles will not change, but each radii will be multiplied by a specific factor..  First, I will design a procedure to create the nth Fibonacci number for a given n.  This procedure will require recursion, as the next Fibonacci number is created by adding the two numbers immediately preceding it, beginning with zero and one as the first two numbers of the sequence.  Another procedure will create the fractal, curved lines required to create the desired pattern. This procedure will use recursion, with a kernel procedure, and repeatedly apply clockwise and counterclockwise quarter-circles of radius which is the radius of the non-fractal quarter-circle desired divided by fractal-num, where fractal-num is defined to be the number of quarter-circles in the fractal desired.  Fractal-num will be determined  by the parameter n mod seven, five, nine, or eleven, depending upon the direction of the desired spiral.  The procedure “turtle-set-color!” will be used in order to change the color of the path.  The modulus function will be used to create the color, which will be created by the “irgb” function, and will be entered for each component, with bases thirty-three, twenty-eight, and thirty-one for the color components red, green, and blue respectively, in order to create a variety of colors that can be created.   As these three numbers are relatively prime to each other, the first repeat of the color possible will be at n equals thirty-three times twenty-eight times thirty-one, or twenty-eight thousand, six hundred and forty four.  Finally, the ground of the image will be created by defining a drawing of a circle of radius determined by the maximum extent of the spiral, whose color is the complement of the color for that drawing, computed by adding one-hundred and twenty-eight to each of the components of the color.  This drawing will then be rendered onto the image, using "drawing-render!"  The modulus function will also be used to define the extent to which the Fibonacci Spiral extends, by controlling the final Fibonacci number to be used for the final radius.  The number k will determine the limit of the Fibonacci-spiral, with k defined to be five plus n mod two.  As there are twenty-eight thousand six hundred and forty-four possible colors created, and none of the colors before this values can be repeats, the color variation guarantees well over one thousand images will be produced.  While the drawing-render-created circle can easily be adjusted so that the width of the circle equals the width of the image and the height of the circle equals the height of the image, the spiral can only be adjusted to be inside and near the edge of the image.  This is required because the spiral is created using turtles that create an image using pixels, and the spiral thus has no easily accessible width and height that can be adjusted to stretch the image.