; For more practice with definitions and expressions let's make a tower of pandas.
; We will place a restriction on ourselves that will implicitly give us some
; experience with exponential growth and binary representation (two concepts
; important in CS which we will discuss later in the course).
(require picturing-programs)
; We named this image 'pandy'.
; When the tower we were making was too large for the projector to show, we came
; back to this definition and put in the scaling. Because we were using the name
; everywhere, all the expressions produced new values.
(define pandy (scale 1/4
))
; The next expression is quite complex.
; Exercise: name parts of it to build up the final result, similar to what we did
; with Kody in the previous document.
(define one (crop-left
(crop-bottom
(crop-top
(crop-right pandy
(round (* 1/4 (image-width pandy))))
(round (* 1/5 (image-height pandy))))
(round (* 1/8 (image-height pandy))))
(round (* 1/10 (image-width pandy)))))
; The function 'round' takes a number and rounds it to the nearest whole number.
; For example:
(round 10.4) ; Produces 10.
(round 12345/104) ; Produces 119 (not obvious, I looked at the Interactions area).
; To build the tower of pandas let's restrict ourselves to making each row without
; using the same name twice to build the row (for fun now, and reasons we will
; discuss later in the course).
(define two (beside one one))
(define four (beside two two))
(define eight (beside four four))
; The next expression produces the tower, using the previous definitions.
; I have lined up the uses of 'four', 'two', and 'one' vertically in this document
; but normally that would be bad style for writing an expression.
(above
one
two
; (beside one one one) violates our self-imposed rule
(beside
two one)
; (beside one one one one) another violation
; (beside one one two) another violation
; (beside two two) another violation
four
(beside four
one)
(beside four two)
(beside four two one)
eight)
; Exercise: put more expressions into that expression to produce a tower with
; fifteen rows.
; The bottom row will be produced by:
(beside eight four two one)
; Expressing sixteen with one, two, four, and eight requires repeating at least one
; of those numbers. So sixteen would be the next number of pandas we name:
(define sixteen (beside eight eight))