Perspectives and Concentric Shapes

Triangle of "hi":

FOR [i 1 30] [

REPEAT :i [TYPE "hi]

PRINT []

]

Note: Refer to Chapter 1 (or see Appendix A) to understand the difference between TYPE and PRINT.

Cone (concentric circles):

ERASE "dcircle

TO dcircle :size ; size is the diameter

REPEAT 360 [FD :SIZE*3.14159/360 RT 1]

END

REPEAT 20 [

dcircle 20+(REPCOUNT*10)

]

Spiral of squares:

This involves drawing squares of increasing size and turning a few degrees after each square.

HT SETPENSIZE 1 FOR [i 5 105] [

square :i RT 5

]

HT SETPENSIZE 1 REPEAT 100 [

square 5+REPCOUNT RT 5

]

Spiral using semi-circles:

ERASE "semi.circle

TO semi.circle :size

REPEAT 180 [FD :size/360 RT 1]

END

Continually draw semi-circles each time increasing the size by a little, and thus get a spiral.

FOR [i 1 25] [

semi.circle 50+:i*20

]

Telescopic arrangement of squares:

This program has two interesting variations: one is obviously the size of squares, which we know how to implement using counters. The second variation is in the color of squares. Since we know the color code varies from 1 to 15, we can once again use a counter to get the series of colors.

ERASE "square

TO square :size

REPEAT 4 [FD :size RT 90]

END

ERASE "jump

TO jump :x :y

PU FD :y RT 90

FD :x LT 90 PD

END

ERASE "pattern

TO pattern :n1 :size

REPEAT :n1 [

BK :size*REPCOUNT/2

square :size*REPCOUNT

FD :size*REPCOUNT/2

jump (:size*REPCOUNT/2) 0

SETPC REPCOUNT

]

END

CS HT SETBG 7 SETPC 0 SETPENSIZE 2

jump -300 0

pattern 8 20

Pyramid of triangles:

The procedure to draw a filled triangle is quite straightforward:

ERASE "triangle

TO triangle :size

REPEAT 3 [FD :size RT 120]

END

ERASE "ftriangle

TO ftriangle :size

triangle :size

RT 30 PU FD :size/3 PD FILL BK :size/3 LT 30

END

Next, we should figure out how to get a row of triangles.

Row of 3 triangles, First cut (with plain instructions):

RT 30 ftriangle 100 LT 30

RT 90 FD 100 LT 90

RT 30 ftriangle 100 LT 30

RT 90 FD 100 LT 90

RT 30 ftriangle 100 LT 30

RT 90 FD 100 LT 90

Row of 3 triangles, Second cut (using REPEAT):

REPEAT 3 [

RT 30 ftriangle 100 LT 30

RT 90 FD 100 LT 90

]

Row of triangles, Final cut: (using a procedure)

; Inputs:

; N is the number of triangles,

; Size is the size of each triangle

ERASE "hills

TO hills :n :size

REPEAT :n [

RT 30 ftriangle :size LT 30

RT 90 FD :size LT 90

]

END

Now, we can use this procedure to build a pyramid.

Pyramid of base 3, First cut (using plain instructions):

hills 3 100

LT 30 FD 100 LT 60 FD 200 RT 90

hills 2 100

LT 30 FD 100 LT 60 FD 100 RT 90

hills 1 100

LT 30 FD 100 LT 60 FD 0 RT 90

Pyramid of base 3, Second cut (pseudo-procedure with input):

We will use N to indicate the number of hills in the base and S to indicate the size of each hill. (Note: These are not real Logo instructions yet, because of N and S)

hills N S

LT 30 FD S LT 60 FD (N-1)*S RT 90

hills (N-1) S

LT 30 FD S LT 60 FD (N-2)*S RT 90

hills (N-2) S

LT 30 FD S LT 60 FD (N-3)*S RT 90

Pyramid, Third cut (using REPEAT and REPCOUNT):

REPEAT N [

hills N-REPCOUNT+1 S

LT 30 FD S LT 60 FD (N-REPCOUNT)*S RT 90

]

Now we are ready for conversion to a procedure using N and S as inputs.

The pyramid procedure:

; Inputs:

; N is the number of triangles in the base,

; Size is the size of each triangle

ERASE "pyramid

TO pyramid :N :S

REPEAT :N [

hills :N-REPCOUNT+1 :S

LT 30 FD :S LT 60 FD (:N-REPCOUNT)*:S RT 90

]

RT 30 BK :N*:S LT 30

END

The following program will draw the pyramids.

CS HT SETPENSIZE 2 SETBG 7

jump -350 -100 SETPC 12 pyramid 3 50

jump 200 0 SETPC 13 pyramid 4 50

jump 250 0 SETPC 14 pyramid 5 50

Self-study: Write the same program using the FOR command instead of REPEAT.

Peacock feathers:

This is not really how a peacock feather looks, but we have only tried to mimic the colors.

This program uses the following procedures:

ERASE "Q.dcircle

TO Q.dcircle :size ; size is the diameter

REPEAT 90 [FD :size*3.14159/360 RT 1]

END

ERASE "petal

TO petal :size ; size is diameter (of the full circle)

Q.dcircle :size

RT 90

Q.dcircle :size

RT 90

END

A single feather: (we have put a gap by skipping a few petals)

CS SETBG 7

SETPC 13 REPEAT 10 [petal 50 + (5*REPCOUNT)]

SETPC 11 REPEAT 10 [petal 125 + (5*REPCOUNT)]

SETPC 14 REPEAT 10 [petal 165 + (5*REPCOUNT)]

SETPC 6 REPEAT 10 [petal 205 + (5*REPCOUNT)]

SETPC 13 REPEAT 3 [petal 245 + (5*REPCOUNT)]

Flower of feathers:

CS SETBG 7

HT ;hiding the Turtle makes the drawing faster

REPEAT 5 [

SETPC 13 REPEAT 10 [petal 50 + (5*REPCOUNT)]

SETPC 11 REPEAT 10 [petal 125 + (5*REPCOUNT)]

SETPC 14 REPEAT 10 [petal 165 + (5*REPCOUNT)]

SETPC 6 REPEAT 10 [petal 205 + (5*REPCOUNT)]

SETPC 13 REPEAT 3 [petal 245 + (5*REPCOUNT)]

RT 360/5

]