gistfile1.scm

(define (runif) (- (* 2 (random)) 1))
(define (rnormish) (+ (runif) (runif) (runif) (runif)))

(define xs0 (build-list 100 (λ _ (rnormish))))
(define ys0 (build-list 100 (λ _ (rnormish))))


(define mags (map (λ (x y) (sqrt (+ (sqr x) (sqr y))))
                    xs0 ys0))
(define xs (map / xs0 mags))
(define ys (map / ys0 mags))

(define ys2 (map (λ (x d) (/ x d 2)) ys0 mags))
(define xs2 (map (λ (x d) (/ x d 2)) xs0 mags))

(plot (list
  (points (map vector xs ys) #:sym 'dot #:size 20)
  (points (map vector xs2 ys2))
) #:title "Cannot separate these with a line")

(plot3d (list
  (points3d (map (λ (x y) (vector (sqr x) (* (sqrt 2) x y) (sqr y))) xs ys) #:sym 'dot #:size 20 #:label "x^2 + y^2 = 1")
(surface3d (λ (x y) (- 0.5 x)) -1 1 -1 1
                           #:label "z = 0.5 - x" #:alpha 0.5 #:color 'yellow)
  (points3d (map (λ (x y) (vector (sqr x) (* (sqrt 2) x y) (sqr y))) xs2 ys2) #:label "x^2 + y^2 = 0.5")
) #:title "Transform x,y to <x^2, sqrt(2)*x*y, y^2>" #:angle 346 #:altitude 13)