Basic Graphics #7 - Scroll

7.  SCROLL

SCROLL  #1

 

 

SAVE AS

>>> import turtle

>>>

>>> Pt = turtle.Turtle()

>>>

>>> def SquareArc(radius):

     n = radius/57.35

     a = n/2

     for i in range(4):

          Pt.forward(radius)

          Pt.right(90)

     Pt.forward(a)

     Pt.right(1)

     for i in range(89):

          Pt.forward(n)

          Pt.right(1)

     Pt.forward(a) 

>>>

>>> Pt.forward(50)

>>> Pt.right(90)

>>>

>>> SquareArc(50)

>>> SquareArc(50)

>>>

>>> SquareArc(100)

>>> SquareArc(100)

>>>

>>> SquareArc(150)

>>> SquareArc(150)

>>>

>>> SquareArc(200)

>>> SquareArc(200)

>>>

>>>

>>> turtle.done()

>>> 

SAVE

Firstly,

the Pt has been positioned where the first arc will eventually start.

Then,

2 SquareArcs have been drawn with the initial radius of    50,

And then,

2 SquareArcs have been drawn with the increased radius of    + 50,

And so on.

 

This arrangement of the SquareArcs produces the Scroll pattern.

VARIABLES

 

 

Variables are amounts, in the program, which can change / vary.

 

Number of pixels, and,

Number of degrees,

are variables.

 

We can write variables into items in the program, within the parentheses    ( )    ,

as in the generalised versions of the previous programs.

Where, they will only apply to the item that they are attached to, such as –

 

Pt.forward(number of pixels)

Pt.right(number of degrees)

  

We can also write the variables into the name of a mechanism,

within the parentheses    ( )    .

But, then they will apply to the whole mechanism, such as –

 

SquareArc(radius)

 

Here, the variable is -

            radius

  

Using variables, we can simplify  Scroll  #1, into  Scroll  #2, below -

SCROLL  #2

 

 

SAVE AS

>>> import turtle

>>>

>>> def SquareArc(radius):

     n = radius/57.35

     a = n/2

     for i in range(4):

          Pt.forward(radius)

          Pt.right(90)

     Pt.forward(a)

     Pt.right(1)

     for i in range(89):

          Pt.forward(n)

          Pt.right(1)

     Pt.forward(a)

>>> def Scroll(radius, radius_increase, t):

      nht = 2*t

      for i in range(nht):

          for i in range(2):

              SquareArc(radius)

          radius = radius + radius_increase

         

>>>

>>> Pt.forward(50)

>>> Pt.right(90)

>>>

>>> Scroll(50, 50, 2)

>>>

>>>

>>> turtle.done()

>>>

SAVE

TILE

The SquareArc  can be called a  “tile”,

in that, all the elements within it are connected,

and it can move as one unit.

 

ARRANGEMENT

This arrangement of the SquareArcs,

using the mechanism -

            Scroll(radius, radius_increase, t)

produces the Scroll pattern.

 

 

Here, in Scroll(radius, radius_increase, t),

radius  =  same radius as in SquareArc(radius)

radius_increase  =  increase in the radius after drawing each set of 2 SquareArcs

                               (The bottom bar _  joins the two words, so that the computer knows it is

                                one item, not two)

t  =  number of complete turns / cycles of the scroll that is required

nht  =  number of half turns of the scroll,

            which is the number of sets of  2  SquareArcs

 

Firstly,

the Pt has been positioned where the first arc will eventually start.

 

For,

Each turn / cycle needed of the scroll,

there needs to be -

            2  x  t    half turns / sets of  2  SquareArcs 

 

But,

after each set is completed,

there needs to be an increase in the radius,

to make the next set larger.

This is achieved by using the equation –

            (outside the “for” loop for the set of  2  SquareArcs,

            by tabbing it backwards in line with the beginning of that loop)

  

            radius  =  radius  +  radius_increase

           

            The computer can understand this type of equation, as saying –

 

                        new radius  =  previous radius  +  radius_increase

 

            In this mechanism, the radius increases by its original amount, each time,

            which is said to be a  “regular”  increase -  that is, “the same” increase each time.

(c) Katherine Stuart 2020

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