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Christmas decoration, snowflakes and rotational symmetry

Christmas decoration, snowflakes and rotational symmetry#

This guide will show you how to decorate for Christmas with Python-embroidered ornaments. The image below shows an example of the decorations we will create through turtle programming.

An embroidered snowflake

A classic choice of motive when decorating Christmas ornaments is a snowflake. What is it about the appearance of snowflakes that makes them so decorative?

../_images/SIA-SIA2013-09130.jpg

Snøfnugg (image av Wilson Alwyn Bentley (1865-1931)).#

If we inspect the crystal closer, we can see that symmetry is one of its key features. Precisely, we can see that it has rotational symmetry, which means that it looks the same (except for small “flaws”) when we rotate it. Rotational symmetry is decorative and efficient and is commonly found in nature, mathematics, design, and art.

../_images/pexels-julia-volk-7293094.jpg

Nature#

Starfish (image by Julia Volk).

../_images/3-7_kisrhombille.svg

Mathematics#

Illustration of a mathematical concept (illustration by Parcly Taxel)

../_images/pexels-andreea-ch-1040895.jpg

Art#

A room decorated with colourful tiles (image by Andreea Ch)

../_images/pexels-humphrey-muleba-2271568.jpg

Technology#

Drone (image by Humphrey Muleba)

Decorate for Christmas with Python-embroidered snow crystals!#

Embroider a line#

Start by copying the code below into your code editor and run it. What image is drawn on the screen?

1from turtlethread import Turtle
2
3needle = Turtle()
4with needle.running_stitch(50):
5    needle.forward(100)
6
7needle.visualise()
Result from the code above. A horisontal blue line with three short vertical lines, one on end of the horisontal line and one in the middle.

Let’s go through the code line for line:

Line 1:

Imports Turtle from the turtlethread library. This can be thought of as asking Python to go in the tool shed (turtlethread), collect the tool (Turtle) we need, and place it on our workbench.

Line 3:

Uses the Turtle command to create a Turtle object and save it in a variable named needle. This is what we will use for embroidery.

Line 4:

Tells what type of stitch we will use. To read more about different stitches in turtlethread, click here.

Line 5:

Tell the needle to move 100 steps forward. Notice that this code is indented one level under the with needle.running_stitch(50):, meaning that the needle will create stitches as it moves.

Line 7:

Calls the needles visualise method. This method uses turtle to draw a visualisation of how the embroidery will look and is a nice way to see if your pattern looks right before you try to embroider it onto fabric.

Lines 3 and 6:

Are empty. Empty lines are used to make the code cleaner and easier to read, but is ignored by the program and removing them has no effect on the output.

Try it yourself:

  • Modify the code to use stitches that are 30 steps in length per stitch. Rerun the program, can you tell the difference?

  • Modify the code to make the needle move 90 steps forward instead of 100 steps

Click here to see how the finished code should look:
1from turtlethread import Turtle
2
3needle = Turtle()
4with needle.running_stitch(30):
5    needle.forward(90)
6
7needle.visualise()
Result from the code above. A horisontal blue line with four short vertical lines with equal spacing between each of them.

Attention

Make sure your code matches the finished code above before you proceed.

Turn right#

We want the “arms” of the crystal to have “branches”. For this, we need to rotate the needle, which we can do with the right command. The below program draws a branch with a 45-degree rotation and a length of 90 steps:

 1import turtlethread
 2
 3needle = turtlethread.Turtle()
 4with needle.running_stitch(30):
 5    # Move forward a little bit
 6    needle.forward(90)
 7
 8    # Draw a "branch" that points a little downwards
 9    needle.right(45)
10    needle.forward(90)
11
12needle.visualise()
Result from the code above. A horisontal blue line and a short diagonal line that starts in the right end of the horisontal line. The lines have small lines equally spaced across them.
Lines 5 and 8:

Starts with a # symbol, meaning that these lines contain comments that Python will ignore. Comments like these are used to keep the code organised with short explanations.

Line 9:

Rotate the turtle 45 degrees to the right.

Try it yourself:

  • Run the program and see what’s drawn on the screen

  • Modify the code, so the branch is rotated 30 degrees instead of 45

  • Modify the code, so the branch has a length of 60 instead of 90.

Klikk her for å se programmet slik det skal være om du har gjort det rett:
 1import turtlethread
 2
 3needle = turtlethread.Turtle()
 4with needle.running_stitch(30):
 5    # Move forward a little bit
 6    needle.forward(90)
 7
 8    # Draw a "branch" that points a little downwards
 9    needle.right(30)
10    needle.forward(60)
11
12needle.visualise()
Result from the code above. A horisontal blue line and a short diagonal line that starts in the right end of the horisontal line. The lines have small lines equally spaced across them.

Attention

Make sure your code matches the finished code above before you proceed.

Complete the snowflake arm#

After drawing a branch, we must move backwards and rotate back to continue the arm. For this, we can use backward and left:

 1import turtlethread
 2
 3needle = turtlethread.Turtle()
 4with needle.running_stitch(30):
 5    # Move forward a little bit
 6    needle.forward(90)
 7
 8    # Draw a "branch" that points a little downwards
 9    needle.right(45)
10    needle.forward(60)
11    needle.backward(60)
12    needle.left(45)
13
14    # Move forward a little bit more
15    needle.forward(90)
16
17needle.visualise()
Result from the code above. A horisontal blue line and a short downwards facing diagonal line that starts in the middle of the horisontal line. The lines have small lines equally spaced across them.

Prøv selv:

  • Run the program and see what’s drawn on the screen

  • Why are the numbers on lines 10 and 11 equal? Is this important? Why/why not?

We’ll finish the “arm” by moving backwards and drawing a branch on the other side. It’s important that we end with the needle in the same position and pointing in the same direction as we started:

 1import turtlethread
 2
 3needle = turtlethread.Turtle()
 4with needle.running_stitch(30):
 5    # Move forward a little bit
 6    needle.forward(90)
 7
 8    # Draw the first "branch" pointing a little downwards
 9    needle.right(30)
10    needle.forward(60)
11    needle.backward(60)
12    needle.left(30)
13
14    # Move forward and then back again
15    needle.forward(90)
16    needle.backward(90)
17
18    # Draw the second "branch" pointing a little upwards
19    needle.left(30)
20    needle.forward(60)
21    needle.backward(60)
22    needle.right(30)
23
24    # Move backwards to the starting point
25    needle.backward(90)
26
27needle.visualise()
Result from the code above. A long horisontal blue line and two diagonal lines that start in the middle of the horisontal line, one pointing downwards and one pointing upwards. All three lines have small lines across to represent stitches with equal distance between each stitch.

Try it yourself

  • Run the code and see what is drawn on the screen.

  • What does line 19 to 22 do?

Attention

Make sure your code matches the finished code above before you proceed.

Use loops to form a snowflake#

Now we have code to instruct are needle-turtle to embroider one arm of a snowflake. However, most snowflakes have multiple arms. So, to draw a full flake, we need to repeat these commands multiple times. For this, we can use a loop. If you want to read more about loops in Python you can click here, but for now you just need to know that we can draw four arms with a for loop like so:

 1import turtlethread
 2
 3needle = turtlethread.Turtle()
 4with needle.running_stitch(30):
 5
 6    for arm in range(4):
 7        # Move forward a little bit
 8        needle.forward(90)
 9
10        # Draw the first "branch" pointing a little downwards
11        needle.right(45)
12        needle.forward(60)
13        needle.backward(60)
14        needle.left(45)
15
16        # Move forward and then back again
17        needle.forward(90)
18        needle.backward(90)
19
20        # Draw the second "branch" pointing a little upwards
21        needle.left(30)
22        needle.forward(60)
23        needle.backward(60)
24        needle.right(30)
25
26        # Move backwards to the starting point
27        needle.backward(90)
28
29        # Rotate 90 degrees to the right to draw four branches
30        needle.right(90)
31
32needle.visualise()
Result from the code above. A snowflake with four "arms". Each arm is identical to that in the previous image.
Line 6:

Starts a for loop and lets Python know that everything in this loop should happen 4 times. Notice that lines 7-20 have been indented an extra level. This tells Python that these lines are inside the loop and should be repeated for each loop repetition.

Line 30:

Tells the turtle to rotate 90 degrees for each loop repetition. This rotation is necessary so we don’t draw all four arms on top of each other.

Try it yourself:

  • Run the program and see what is drawn on the screen

  • Why is there a 90-degree rotation on line 30? What happens if you change it to 60 instead?

  • Modify the code to draw a snowflake with 6 arms instead of 4.

Click here to see how the finished code should look:
 1import turtlethread
 2
 3needle = turtlethread.Turtle()
 4with needle.running_stitch(30):
 5
 6    for arm in range(6):
 7        # Move forward a little bit
 8        needle.forward(90)
 9
10        # Draw the first "branch" pointing a little downwards
11        needle.right(30)
12        needle.forward(60)
13        needle.backward(60)
14        needle.left(30)
15    
16        # Move forward and then back again
17        needle.forward(90)
18        needle.backward(90)
19    
20        # Draw the second "branch" pointing a little upwards
21        needle.left(30)
22        needle.forward(60)
23        needle.backward(60)
24        needle.right(30)
25
26        # Move backwards to the starting point
27        needle.backward(90)
28
29        # Rotate 60 degrees to the right to draw six branches
30        needle.right(60)
31
32needle.visualise()
Result from the code above. A snoflake with six "arms". Otherwise equal to the image above.

Attention

Make sure your code matches the finished code above before you proceed.

Now we have code to draw a complete snowflake!

Try it yourself:

Use code to draw your own snowflake with rotational symmetry. Below is a gallery with some examples you can use as a starting point or just for inspiration!

Create an ornament with your snowflake#

An action shot of the embroidery machine making a snowflake.

To create an ornament with the snowflake embroidery you first need to save the pattern as an embroidery file. You can do this by adding

needle.save("snowflake.jef")

at the end of your script. Note that we here used the .jef extension, which we have found to work well with the Bernina 500 machine, but you might want to use another filetype for your machine (e.g. snowflake.pes). Once you’ve created the embroidery file, you can follow these instructions:

  1. Embroider one or two snowflakes, depending on whether you want a snowflake on both sides of the ornament.

  2. Place the two fabric pieces on top of each other so the embroidery patterns are on top of each other and pointing outwards.

  3. Sew the pieces together (either by hand or by drawing a circle with turtlethread).

Example snowflakes#

Snowflake 1

Two arms of different snowflakes on top of each other, with a 30 degree rotation between the arms. One of the arm-types consists of one long line with three circles of varying size on top of each other at the end. The other arm-type consists of a small line with a small circle at the end.
SnowflakeTwo different snowflakes on top of each other, making a snowflake with 12 arms of alternating type. One of the arm-types consists of one long line with three circles of varying size on top of each other at the end. The other arm-type consists of a small line with a small circle at the end.
Code for arm
 1from turtlethread import Turtle
 2
 3needle = Turtle()
 4
 5with needle.running_stitch(10):
 6    # Rotate snowflake half a turn
 7    needle.right(30)
 8    
 9    # Draw arm of main snowflake
10    needle.forward(100)
11    needle.right(90)
12    needle.circle(30)
13    needle.circle(20)
14    needle.circle(10)
15    needle.left(90)
16    needle.backward(100)
17    needle.left(60)
18        
19
20    # Rotate 30 degrees before drawing the arm of the second snowflake
21    needle.right(30)
22    # Draw arm of second snowflake
23    needle.forward(40)
24    needle.right(90)
25    needle.circle(10)
26    needle.left(90)
27    needle.backward(40)
28    needle.left(60)
29
30needle.visualise()
Code for snowflake
 1from turtlethread import Turtle
 2
 3needle = Turtle()
 4
 5with needle.running_stitch(10):
 6    # Rotate snowflake half a turn
 7    needle.right(30)
 8
 9    for arm in range(6):    # Draw arms of main snowflake
10        needle.forward(100)
11        needle.right(90)
12        needle.circle(30)
13        needle.circle(20)
14        needle.circle(10)
15        needle.left(90)
16        needle.backward(100)
17        needle.left(60)
18        
19
20    # Rotate 30 degrees before drawing the second snowflake
21    needle.right(30)
22    for arm in range(6):    # Draw arms of second snowflake
23        needle.forward(40)
24        needle.right(90)
25        needle.circle(10)
26        needle.left(90)
27        needle.backward(40)
28        needle.left(60)
29
30needle.visualise()

Snowflake 2

A right angled triangle whose hypothenus is horizontal. The proportion of the triangle's legs to its hypothenus is 3/5 and 4/5.
SnowflakeA snowflake whose six arms are right-angled triangles. It resembles a paper fan.
Code for arm
 1from turtlethread import Turtle
 2
 3needle = Turtle()
 4
 5with needle.running_stitch(10):
 6    needle.forward(40*2)
 7    needle.left(90)
 8    needle.forward(30*2)
 9    needle.left(127)
10    needle.forward(50*2)
11    needle.right(127)
12    needle.right(90)
13    
14    needle.left(60)
15    
16needle.visualise()
Code for snowflake
 1from turtlethread import Turtle
 2
 3needle = Turtle()
 4
 5with needle.running_stitch(10):
 6    for arm in range(6):
 7        needle.forward(40*2)
 8        needle.left(90)
 9        needle.forward(30*2)
10        needle.left(127)
11        needle.forward(50*2)
12        needle.right(127)
13        needle.right(90)
14        
15        needle.left(60)
16    
17needle.visualise()

Snowflake 3

Two arms of different snowflakes on top of each other, with a 30 degree rotation between the arms. Both arms resemble those we made in this tutorial but of different sizes.
SnowflakeTwo different snowflakes on top of each other, making a snowflake with 12 arms of alternating type. Both snowflakes have arms resemble those we made in this tutorial but of different sizes.
Code for arm
 1from turtlethread import Turtle
 2
 3needle = Turtle()
 4
 5with needle.running_stitch(10):
 6    # Draw arm of main snowflake
 7    needle.forward(100)
 8    needle.right(40)
 9    needle.forward(40)
10    needle.backward(40)
11    needle.left(40)
12    needle.forward(30)
13    needle.right(30)
14    needle.forward(20)
15    needle.backward(20)
16    needle.left(30)
17    needle.forward(20)
18
19    needle.backward(20)
20
21    needle.right(-30)
22    needle.forward(20)
23    needle.backward(20)
24    needle.left(-30)
25
26    needle.backward(30)
27
28    needle.right(-40)
29    needle.forward(40)
30    needle.backward(40)
31    needle.left(-40)
32    needle.backward(100)
33    needle.left(60)
34
35    # Rotate 30 degrees before drawing the arm of the second snowflake
36    needle.right(30)
37
38    # Draw arm of second snowflake
39    needle.forward(50)
40
41    needle.right(40)
42    needle.forward(20)
43    needle.backward(20)
44    needle.left(40)
45
46    needle.forward(30)
47    needle.backward(30)
48
49    needle.left(40)
50    needle.forward(20)
51    needle.backward(20)
52    needle.right(40)
53
54    needle.backward(50)
55    needle.left(60)
56
57needle.visualise()
Code for snowflake
 1from turtlethread import Turtle
 2
 3needle = Turtle()
 4
 5with needle.running_stitch(10):
 6    for arm in range(6):  # Draw arm of main snowflake
 7        needle.forward(100)
 8        needle.right(40)
 9        needle.forward(40)
10        needle.backward(40)
11        needle.left(40)
12        needle.forward(30)
13        needle.right(30)
14        needle.forward(20)
15        needle.backward(20)
16        needle.left(30)
17        needle.forward(20)
18
19        needle.backward(20)
20
21        needle.right(-30)
22        needle.forward(20)
23        needle.backward(20)
24        needle.left(-30)
25
26        needle.backward(30)
27
28        needle.right(-40)
29        needle.forward(40)
30        needle.backward(40)
31        needle.left(-40)
32        needle.backward(100)
33        needle.left(60)
34
35    # Rotate 30 degrees before drawing the arm of the second snowflake
36    needle.right(30)
37
38    for arm in range(6):  # Draw arm of second snowflake
39        needle.forward(50)
40
41        needle.right(40)
42        needle.forward(20)
43        needle.backward(20)
44        needle.left(40)
45
46        needle.forward(30)
47        needle.backward(30)
48
49        needle.left(40)
50        needle.forward(20)
51        needle.backward(20)
52        needle.right(40)
53
54        needle.backward(50)
55        needle.left(60)
56
57needle.visualise()
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