You may also like

problem icon

LOGO Challenge - Tiling with Equilateral Triangles

Try making patterns with equilateral triangles

problem icon

Some Spirals and Tessellations

Making spirals with LOGO

problem icon

Serendipity

Can you write LOGO programs for some beautiful irregular tilings?

Spirals and Wallpapers

Stage: 3 Challenge Level: Challenge Level:1

A spiral is defined as:

...a curve formed by a point moving around a fixed point and constantly moving away from or approaching the fixed point.

(p110. HBJ Dictionary of Mathematics compiled by Ken Klaebe)

Consider the following RECURSIVE procedures:

TO SPIR1 :A
IF 200 < :A [STOP]
FD :A RT 45
SPIR1 :A + 1
END


TO SPIR2 :A :ANG
IF 200 < :A [STOP]
FD :A RT :ANG
SPIR2 :A + 1 :ANG
END

TO SPIR3 :A :ANG
IF 200 < :A [STOP]
FD :A RT :ANG
SPIR3 :A + 10 :ANG
END

TO SPIR4 :A :B
FD 30 RT :A
SPIR4 :A + :B :B
END

Experiment, alter the variables and see what conclusions you can come to.

How did your resultant figures fit with the definition above?

How wide a range of spirals can you now draw?

In your research see if you can model two important geometric figures - the Archimedean and equiangular spirals?

More wallpaper patterns

On another theme, you might like to consider the remaining wallpaper patterns. Like the patterns given in previous months, they build on the freize patterns that went before, in that they are obtained from them by introducing a reflection or glide or both. As before each is described according to an international system of coding.

Can you use some elegant programming to replicate these patterns (or with a much more flamboyant motif) and so study this 'small' set of patterns yet further.

p4g - a quarter turn and an added glide. p4m - a quarter turn and added reflection.
p6m - adding a reflection. p3lm -a rotation of 120 degrees.

p3ml - a rotation of 120 degrees followed by a reflection.