Design Statement     The intent of the series is create a visual representation of the idea that one can never get the whole picture,in any situation. In order to capture this, our pictures are structured to look like there is light shining through two holes in a box onto a surface. On this surface, different parts of a pattern are being revealed by the two beams of light. While the pattern will remain the same for the thousand images, only part of it will be shown at a time; that is, one can only see the areas of the pattern that are illuminated by the beams of light. We will vary the color of the lights and the angle the lights are coming through the holes in order to create variety among the series of images; how we do so will contribute to the meaning behind the series.     We will vary the colors by hue: the true color of the pattern will be tinted by the color of the light shining through the hole. The fact that the color of the light tints the pattern represents the inherent bias in any lenses we can look through. In order to get a sense of the color of the pattern, it is best to look at several images with different hues of light, representing the fact that to get a more complete picture of a situation, it is best to look at it through a variety of lenses.     Additionally, we will use value and saturation to contribute to a sense of depth. So that the light behaves how one would expect it to, the light will have a lower value and saturation when on the black backdrop and a higher one coming through the hole and shining on the surface. Where the two beams of light intersect, the color will be the result of adding them together. The background elements, ie. the backdrop and the surface, will be monochrome, particularly varying shades of gray and black. We will make approximately 2/3s of the top of the screen the black backdrop, and the bottom 1/3 the gray surface. The black will create negative space, and the lighter gray, along with the hole, the pattern and the beams of light, will make up the positive space. We want the negative space to outweigh the positive space so it contributes to the weight of the sense of the unknown. In any given image, the lights will also be monochrome, but be brightest at the hole and on the ground, in order to emphasize those two elements and the importance of the pattern on the ground. The pattern itself will be a blend of the color wheel, in order to represent a complex situation.     Having two holes, and therefore two beams of light, represents how sometimes it may be better to look at a situation with another person. Doing so gives one another perspective on the situation, and again, allows for a clearer view of the entire picture. Changing the angle of the light will contribute to the theme of studying a situation from a variety of angles in order to get a more complete picture. Changing the angle also creates the illusion of motion, and subsequently the sense of time passing, so it looks like the pattern is being studied over a period of time. As the parts of the pattern on the surface which the beams of light illuminate will only be a fraction of the entire surface, there should be plenty of variety in changing the location where the light shines on the surface. The convergence of the two lines that make up each respective “beam” of light coming from the hole onto the ground will add to the illusion of depth, as the viewer will naturally want to believe that the beam coming through the hole converges at some point outside of the picture.     The holes will be outlined with sharp lines, forming a clear circle. The beam of light will also have crisp edges, clearly different from the black and gray backgrounds. This conveys the fact that it provides a sharp picture of what it illuminates, but to also demonstrate how limited what we can see is. The division between black backdrop and gray surface will contribute to the illusion of depth, making it look like a horizon. The horizon will not be a clear line; it will be blurred so there isn't a sharp change between the backdrop and the surface. This is to reduce emphasis on the horizon, making it seem more like part of the background, and blur the distinction between the pattern we're looking at and the darkness of the backdrop Technique Statement         Our algorithm will consist of four major steps. First,  we will break n up into 6 values which determine the beam colors and the coordinates of the centers of the beams. Then, we will generate the pattern (parts of which are revealed by the spotlight discussed in the design statement) with some modifications to its inputs based on the size of the image and render it onto the image. With the previously generated values and image-redo! we will generate the background and the two spotlights; in the spotlights, the color of the pattern will be blended with the color of the spotlight. Finally, we will go over the image with image-redo! to add the beams of light and use drawing-render! to add the two holes. The three algorithmic techniques we will be using are using image-compute and image-redo! to create our design, images as sequences of drawing, and numeric recursion to help make these sequences.     In order to build the pattern, we will begin by making a simple geometric drawing using drawing techniques. We will then take these basic drawings and use recursion to build more complex drawings based on the basic ones. We justify using recursion over map because it's more efficient: rather than having to make and modify multiple lists to hold all the positions for the basic drawings and the drawings themselves, then having to apply the position lists to the drawing lists, which would involve going over each list several times, we can write one recursive function which achieves the same result without having to go over the same lists many times.         In order to ensure we can make 1000 images, each beam can be one of three colors and have one of twelve locations. Three colors and twelve locations (2 y values and 6 x values) give each beam 36 distinct states. Since the two beams are independent of each other, every state in the first beam can be combined with each of the 36 states in the other beam to produce a unique combination for the image as a whole. That's 36 squared, or 1296 unique images. But how do we translate the n value, ranging from 0 to 1295, that the user inputs into unique combinations of the six numbers which describe the states of the two beams? First we use n to make 1295 unique combinations of two numbers, each of which ranges from 0 to 35 and describes everything about one beam; we will explain the method by which we do this after we complete the overview of the breakdown of n. Then, for each beam, we break each of those numbers into two more numbers from 0 to 5 using the same method; finally, we take one of the 0 to 5 groups and use relatively prime numbers, 2 and 3, and modulus, to make 6 unique combinations of a number from the set (0, 1) and one from the set (0, 1, 2).     In order to demonstrate the principle behind our method for breaking up the square numbers, 1296 and 36, we will use a simpler example: breaking up a value of n in the range [0, 8] or three squared into a unique combination of two numbers both ranging from 0 to 2. If we think of the n value as denoting a box in a grid, each box has its own unique combination of column and row numbers which are the numbers we are trying to find. ----------------------------------------------------------------------- | Col 0 | Col 1 | Col 2 ----------------------------------------------------------------------- Row 0 | Box 0; | Box 1; | Box 2; | coordinates (0, 0) | coordinates (1, 0) | coordinates (2, 0) ----------------------------------------------------------------------- Row 1 | Box 3; | Box 4; | Box 5; | coordinates (0, 1) | coordinates (1, 1) | coordinates (2, 1) ----------------------------------------------------------------------- Row 2 | Box 6; | Box 7; | Box 8; | coordinates (0, 2) | coordinates (1, 2) | coordinates (2, 2) ----------------------------------------------------------------------- Assume we are just going through the box, going left to right within a row first, and once we have finished the row moving on to the next one. In order to find the column number based on the box number, we can just take the modulus of the box number divided by the number of columns. In order to find the row number, we can take the box number, divide it by the number of rows, and then round down. This method can be expanded to a square of any size.         Using image-compute to build the background and the beams of light uses many of the techniques we learned in the reading “Building Images by Iterating Over Positions.” The holes and the circles on the surface which they spotlight use euclidean-distance to create circles. The sides of the beams of light are linear equations based on tangent lines to the circles. The fading of the gray surface into the black backdrop uses a color blend. The color of the beams of light is stored in HSV, so we can lower the saturation and value when the beams passing through the black backdrop. Some of the HSV techniques are borrowed from Assignment 5.         We will color all of the drawings in the pattern a particular irgb value, such as 1 2 3, so that we can use image-redo! to scan for which parts of the image are the pattern and easily distinguish those from the rest of the image. Based on where the beams of light land, we will either change the color of the pattern. If the pattern is not illuminated by a spotlight, we will change it to the gray of the background. If it is, we will change it to a combination of the patterns true color and the color of the beam of light. The patterns true color will be a rainbow fade going from left to right on the image.