Flower Power
Create a symmetrical fabric design based on a flower motif - and realise it in Logo.
Age
11 to 16
Challenge level
Problem
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Create a design for a patterned fabric based on a flower motif. The motif should show rotational symmetry. The motif should be repeated across the width and length of the fabric in an interesting way which also shows symmetry.
Start by roughing out a design. You may wish to use a real flower for inspiration, or you could start from something more abstract provided it can be recognised as a flower.
When you are happy with your design, use Logo to create a print of the fabric. If you wish to submit your design, include a screenshot and the Logo program you used to create it, together with a summary of the symmetry shown by the motif and by the overall design.
Start by roughing out a design. You may wish to use a real flower for inspiration, or you could start from something more abstract provided it can be recognised as a flower.
When you are happy with your design, use Logo to create a print of the fabric. If you wish to submit your design, include a screenshot and the Logo program you used to create it, together with a summary of the symmetry shown by the motif and by the overall design.
Ideas to think about:
- The number of petals of many flowers is given by the Fibonacci sequence.
- What calculation do you need to do to work out the angle between petals if the flower is to show rotational symmetry?
Windows users can download a free copy of Logo from FMSlogo.
A good free version for Mac users is ACSlogo.
There's a version you can run directly in your browser at http://calormen.com/logo/.
Getting Started
Image
The program consists of four Logo Procedures:
To petal
ht lt 40 repeat 16[fd 4 rt 5] rt 100 repeat 16[fd 4 rt 5] rt 140 end
To flower
repeat 5[petal rt 72] end
To strip
repeat 5[flower pu fd 128 pd] end
To fabric
pu lt 90 fd 300 rt 90 bk 300 pd repeat 5[strip pu rt 90 fd 120 lt 90 bk 560 pd] end
ht lt 40 repeat 16[fd 4 rt 5] rt 100 repeat 16[fd 4 rt 5] rt 140 end
To flower
repeat 5[petal rt 72] end
To strip
repeat 5[flower pu fd 128 pd] end
To fabric
pu lt 90 fd 300 rt 90 bk 300 pd repeat 5[strip pu rt 90 fd 120 lt 90 bk 560 pd] end
Logo commands
ht = hide turtle
lt - left
fd = forward
rt = right
pu = pen up
pd = pen down
bk = back
lt - left
fd = forward
rt = right
pu = pen up
pd = pen down
bk = back
Can you see what each program and each command is doing?
The forward distance of 4 pixels was chosen to give a sensible size of petal. What happens if you change it?
Similarly the angle change of 5 degrees seemed to give a good result. What happens if you change this? And how do you have to change the other angles and the number of repeats if you change it?
The forward and backward instructions in To fabric at the beginning and at the end of the repeat were chosen fairly arbitrarily to give an effective design.
Generalising the program
You can generalise the petal size and hence the size of the finished design by using a variable instead of the length of 4.See if you can work out how to do this: help in using variables.
Can you then generalise for the number of petals in the flower?
Teachers' Resources
It is not envisaged that this problem would be used as a class problem. It is more appropriate for an enthusiastic student or small group of students looking for a challenge to work on independently.
Students who want help in getting going with Logo could try some of the problems in Fast Forward Into Logo or Making Moire Patterns.
Students who want help in getting going with Logo could try some of the problems in Fast Forward Into Logo or Making Moire Patterns.