Analyse these repeating patterns. Decide on the conditions for a periodic pattern to occur and when the pattern extends to infinity.

Find all the periodic cycles and fixed points in this number sequence using any whole number as a starting point.

A spiropath is a sequence of connected line segments end to end taking different directions. The same spiropath is iterated. When does it cycle and when does it go on indefinitely?

Look at how the pattern is built up - in that way you will know how to break the final pattern down into more manageable pieces.

Can you use LOGO to create a systematic reproduction of a basic design? An introduction to variables in a familiar setting.

are somewhat mundane they do pose a demanding challenge in terms of 'elegant' LOGO procedures. This problem considers the eight semi-regular tessellations which pose a demanding challenge in terms of. . . .

Three examples of particular tilings of the plane, namely those where - NOT all corners of the tile are vertices of the tiling. You might like to produce an elegant program to replicate one or all. . . .

Working with recursion. What is going on how does each iteration feen into the next? All within a geometric setting.

Several procedures to think about but there are several things you can do to help yourself such as breaking the procedures down stepwise (rather than into smaller peices) What does the first line do?. . . .

What happens when a procedure calls itself?

Logo helps us to understand gradients of lines and why Muggles Magic is not magic but mathematics. See the problem Muggles magic.

Can you puzzle out what sequences these Logo programs will give? Then write your own Logo programs to generate sequences.

Turn through bigger angles and draw stars with Logo.

Learn to write procedures and build them into Logo programs. Learn to use variables.

This LOGO Challenge emphasises the idea of breaking down a problem into smaller manageable parts. Working on squares and angles.

Creating designs with squares - using the REPEAT command in LOGO. This requires some careful thought on angles

More Logo for beginners. Now learn more about the REPEAT command.

Learn about Pen Up and Pen Down in Logo

More Logo for beginners. Learn to calculate exterior angles and draw regular polygons using procedures and variables.

Write a Logo program, putting in variables, and see the effect when you change the variables.

Using LOGO, can you construct elegant procedures that will draw this family of 'floor coverings'?

Can you use LOGO to create this star pattern made from squares. Only basic LOGO knowledge needed.

A Short introduction to using Logo. This is the first in a twelve part series.

A weekly challenge concerning drawing shapes algorithmically.

This is a complete Logo development system which runs in the Flash Player. It can therefore be used to introduce Logo problems over the web without the need to refer readers to external. . . .

Can you reproduce the design comprising a series of concentric circles? Test your understanding of the realtionship betwwn the circumference and diameter of a circle.

Here are some circle bugs to try to replicate with some elegant programming, plus some sequences generated elegantly in LOGO.

In LOGO circles can be described in terms of polygons with an infinite (in this case large number) of sides - investigate this definition further.

Thinking of circles as polygons with an infinite number of sides - but how does this help us with our understanding of the circumference of circle as pi x d? This challenge investigates. . . .

This LOGO challenge starts by looking at 10-sided polygons then generalises the findings to any polygon, putting particular emphasis on external angles

Pentagram Pylons - can you elegantly recreate them? Or, the European flag in LOGO - what poses the greater problem?

The challenge is to produce elegant solutions. Elegance here implies simplicity. The focus is on rhombi, in particular those formed by jointing two equilateral triangles along an edge.

Recreating the designs in this challenge requires you to break a problem down into manageable chunks and use the relationships between triangles and hexagons. An exercise in detail and elegance.

Explore patterns based on a rhombus. How can you enlarge the pattern - or explode it?

Moiré patterns are intriguing interference patterns. Create your own beautiful examples using LOGO!

Remember that you want someone following behind you to see where you went. Can yo work out how these patterns were created and recreate them?

Create a symmetrical fabric design based on a flower motif - and realise it in Logo.

Explore this how this program produces the sequences it does. What are you controlling when you change the values of the variables?

Overlaying pentominoes can produce some effective patterns. Why not use LOGO to try out some of the ideas suggested here?

This is the second in a twelve part introduction to Logo for beginners. In this part you learn to draw polygons.

Just four procedures were used to produce a design. How was it done? Can you be systematic and elegant so that someone can follow your logic?

This part introduces the use of Logo for number work. Learn how to use Logo to generate sequences of numbers.

Can you recreate these designs? What are the basic units? What movement is required between each unit? Some elegant use of procedures will help - variables not essential.

Learn how to draw circles using Logo. Wait a minute! Are they really circles? If not what are they?

See if you can anticipate successive 'generations' of the two animals shown here.