Snowflakes are based on sixfold rotational symmetry. To produce a sixfold rotation use this code:

repeat 6 [ repeat 3 [ fd 100 rt 120] rt 60]

This draws 6 triangles set inside a hexagon.

Now try it with something a bit more interesting than a triangle.

cs ht repeat 6 [ repeat 6 [fd 100 rt 60] rt 60]

This draws 6 overlapping hexagons.

Use print screen and paste to get this pattern into paint and then colour it in.

If you alter the angles and repeat numbers but maintain the sixfold symmetry then you can obtain lots of nice shapes to colour in.

cs ht repeat 12 [ repeat 6 [fd 100 rt 45] rt 30]

Use print screen and paste to get this pattern into paint and then colour it in.

Koch Fractal

This is an example of a fractal that is generated by taking each line segment of the existing curve and replacing it with a specific set of line segments.
The process is then repeated until the desired depth is reached. Each line segment of the replacement pattern is itself replaced and so on.
Many interesting curves can be generated by this process. All you need to do is alter the code for the collection of lines that are used in the replacement process.

This is the code for the Koch fractal.

to koch :size :level
if :level = 0 [ fd :size stop]
koch :size/3 :level-1 rt 60
koch :size/3 :level-1 lt 120
koch :size/3 :level-1 rt 60
koch :size/3 :level-1
end

You can test this program by typing
koch 200 3

Turn this into a snowflake by using the code below.

cs ht repeat 6 [ koch 200 3 rt 60]

Use print screen and paste to get this pattern into paint and then colour it in.

Altering angles can give more 'realistic' patterns.

cs ht repeat 6 [repeat 3 [ koch 100 2 rt 60]rt 120]

Use print screen and paste to get this pattern into paint and then colour it in.

Alter the pen colours and size to make it even more fun.

Use the "set" menu to change the colour of lines and the screen.

Groovy Borders

Use the "set" menu to change the colour of lines and the screen. Or use the code below and change the numbers in the setpensize and setpencolor commands.

setpensize [1 1] setpencolor 8 repeat 5 [fd 100 rt 72]

Draw the same polygon, over and over again, with gradually thinner lines in different colours

Swirling Shapes

Make a polygon and then put the polygon code into a repeat loop so that you can draw lots of copies of it gradually turning through 360 degrees.

cs ht repeat 20 [ repeat 5 [fd 100 rt 72] rt 18]

Stellations.

Draw a repeating polygon pattern but then alter the code for the repeat and the polygon.
The first example swaps the 18 and 72 degree angles around. The second one uses 36 degrees instead of 18. If you want your pattern to form a closed loop then the angles used must be related to those of the basic polygon that you have used

cs ht repeat 20 [ repeat 5 [fd 100 rt 18] rt 72]
cs ht repeat 20 [ repeat 5 [fd 100 rt 36] rt 72]