#lang racket (require gigls/unsafe) ;;; Procedure: ;;; image-series ;;; Parameters: ;;; n, an integer ;;; width, an integer ;;; height, an integer ;;; Purpose: ;;; Creates an image which depends on n with the specified width and hieght ;;; Produces: ;;; fractal-plant, an image ;;; Preconditions: ;;; n is an integer between 0 and 999 inclusive ;;; width is a positive integer ;;; height is a positive integer ;;; Postconditions: ;;; fractal-plant is an image ;;; Each value of n produces a distinct fractal-plant. ;;; fractal-plant satisfies (image-width fractal-plant)=width ;;; fractal-plant satisfies (image-height fractal-plant)=height ;;; fractal-plant is composed of a vertical gradient 'background', ;;; and a 'fractal' resembling a plant in the foreground ;;; 'background' is a smooth blend between two colors, which are determined by ;;; n modulo 7. ;;; 'fractal' begins at the (0, height) coordinate, and grows at an angle ;;; determined by width and height. ;;; 'fractal' is a fractal which is iterated (n modulo 5) + 2 times. ;;; The color of the ends of 'fractal' is determined by n modulo 11. ;;; The size of 'fractal' is determined by width, height, and n modulo 3. ;;; Props: ;;; The following website provided our inspiration for fractal plant: ;;; http://en.wikipedia.org/wiki/L-system ;;; Ajuna Kyaruzi helped us figure out how to return an image without showing it. ;;; In writing the color-blend local helper procedure, we referred to code using ;;; image-compute-pixels! from the lab on building images by iterating over ;;; positions to get ideas for how to use image-recompute! to implement a ;;; procedure to produce a vertical gradient for our background. The code from ;;; the lab was written by Braden Brown, Gregory Garcia, and China Mauck. (define image-series (lambda (n width height) (letrec ; Generate a two-color blend that will be used as the background for fractal-plant. ([color-blend (λ (color1 color2 width height) (let ([canvas (image-new width height)] [color1 (color-name->irgb color1)] [color2 (color-name->irgb color2)]) (image-select-all! canvas) (image-recompute! canvas (λ ( col row) ; Take the difference between each component of color1 and color2 and divide ; by height to determine the increment per row. (irgb (- (rgb-red color1) (* (/ (- (rgb-red color1) (rgb-red color2)) height) row)) (- (rgb-green color1) (* (/ (- (rgb-green color1) (rgb-green color2)) height) row)) (- (rgb-blue color1) (* (/ (- (rgb-blue color1) (rgb-blue color2)) height) row)))))))] ; Implement color-blend to generate the seven possible backgrounds for fractal-plant. ; The pair color1 and color2 that is used is determined by n modulo 7. [background (cond [(= 0 (modulo n 7)) (color-blend "steelblue" "navy" width height)] [(= 1 (modulo n 7)) (color-blend "gold" "lawngreen" width height)] [(= 2 (modulo n 7)) (color-blend "skyblue" "seagreen" width height)] [(= 3 (modulo n 7)) (color-blend "dodgerblue" "forestgreen" width height)] [(= 4 (modulo n 7)) (color-blend "orangered" "orange" width height)] [(= 5 (modulo n 7)) (color-blend "purple" "seagreen" width height)] [(= 6 (modulo n 7)) (color-blend "black" "navy" width height)])] ; Add a turtle to the bottom left corner of background. [Atuin (turtle-teleport! (turtle-new background) 0 height)] ; Define the distance the turtle will travel in the first step of fractal-plant by ; using predetermined ratios that scale appropriately with the width and height of the image. ; The three possible distances depend on n modulo 3. [distance (cond [(= 0 (modulo n 3)) (* (sqrt (+ (expt ( * height 0.27189233611099495) 2) (expt ( * width 0.12678547852220984) 2))) (/ 2 3))] [(= 1 (modulo n 3)) (sqrt (+ (expt ( * height 0.27189233611099495) 2) (expt ( * width 0.12678547852220984) 2)))] [(= 2 (modulo n 3)) (* (sqrt (+ (expt ( * height 0.27189233611099495) 2) (expt ( * width 0.12678547852220984) 2))) (/ 4 3))])] ; Define the initial angle the turtle turns to be an appropriate angle for the size of the image. ; angle is dependent on the width and height of the image. [angle (* (/ 180 pi) (atan (/ ( * height 0.27189233611099495) ( * width 0.12678547852220984))))] ; Choose the color for the ends of fractal-plant based on n modulo 11. [color (list-ref (list "pink" "thistle" "lemonchiffon" "cornflowerblue" "purple" "crimson" "yellow" "coral" "maroon" "violet" "steelblue") (modulo n 11))] ; Define the fractal, using previous definitions and procedures. [fractal-plant (λ (turtle distance k) ; Set the brush to an appropriate size: 1 when k=0, or 2 when k>0. (turtle-set-brush! turtle "2. Hardness 100" (min 2 (+ k 1))) ; Set the color of the different iterations of fractal plant. (cond [(= k 0) (turtle-set-color! turtle color)] [(= k 1) (turtle-set-color! turtle "yellowgreen")] [else (turtle-set-color! turtle "olive")]) ; Turn the turtle counterclockwise the appropriate angle to begin the fractal iteration. (turtle-turn! turtle (- 0 angle)) ; Move the turtle forward to begin drawing the fractal. (turtle-forward! turtle distance) ; If k>0, create three clones of turtle, which move and turn in distinct ways to create ; the fractal. For each of the four turtles, recursively call fractal-plant with k-1 iterations and distance/2. ; If k=0, move the turtle forward half the given distance. (cond [(= 0 k) (turtle-forward! turtle (/ distance 2))] [else (for-each fractal-plant (list (turtle-turn! (turtle-clone turtle) angle) (turtle-turn! (turtle-forward! (turtle-clone turtle) (/ distance 3)) (+ angle 15)) (turtle-turn! (turtle-forward! (turtle-clone turtle) (- 0 (/ distance 5))) (+ angle 20)) (turtle-turn! turtle (- angle 25))) (make-list 4 (/ distance 2)) (make-list 4 (- k 1)))]))]) ; Implement fractal-plant with iterations between 2 and 6, inclusive, dependent ; on n modulo 5. (fractal-plant Atuin distance (+ (modulo n 5) 2)) background)))