Find all the periodic cycles and fixed points in this number
sequence using any whole number as a starting point.
What happens when a procedure calls itself?
Recursion and the some beautiful results
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?. . . .
A Short introduction to using Logo. This is the first in a twelve part series.
Explore this how this program produces the sequences it does. What
are you controlling when you change the values of the variables?
Pentagram Pylons - can you elegantly recreate them? Or, the
European flag in LOGO - what poses the greater problem?
Here are some circle bugs to try to replicate with some elegant
programming, plus some sequences generated elegantly in LOGO.
Learn the Logo programming language from scratch by working through some mathematical challenges both geometrical and numerical.
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.
Remember that you want someone following behind you to see where
you went. Can yo work out how these patterns were created and
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.
Can you puzzle out what sequences these Logo programs will give? Then write your own Logo programs to generate sequences.
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?
Analyse these repeating patterns. Decide on the conditions for a
periodic pattern to occur and when the pattern extends to infinity.
Just four procedures were used to produce a design. How was it
done? Can you be systematic and elegant so that someone can follow
Can you use LOGO to create this star pattern made from squares.
Only basic LOGO knowledge needed.
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.
See if you can anticipate successive 'generations' of the two
animals shown here.
This LOGO challenge starts by looking at 10-sided polygons then
generalises the findings to any polygon, putting particular
emphasis on external angles
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 to write procedures and build them into Logo programs. Learn to use variables.
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. . . .
Learn how to draw circles using Logo. Wait a minute! Are they really circles? If not what are they?
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. . . .
A weekly challenge concerning drawing shapes algorithmically.
Create a symmetrical fabric design based on a flower motif - and realise it in Logo.
Moiré patterns are intriguing interference patterns. Create your own beautiful examples using LOGO!
Creating designs with squares - using the REPEAT command in LOGO.
This requires some careful thought on angles
This part introduces the use of Logo for number work. Learn how to use Logo to generate sequences of numbers.
This LOGO Challenge emphasises the idea of breaking down a problem
into smaller manageable parts. Working on squares and angles.
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.
More Logo for beginners. Learn to calculate exterior angles and draw regular polygons using procedures and variables.
Explore patterns based on a rhombus. How can you enlarge the
pattern - or explode it?
Overlaying pentominoes can produce some effective patterns. Why not
use LOGO to try out some of the ideas suggested here?
In LOGO circles can be described in terms of polygons with an
infinite (in this case large number) of sides - investigate this
Using logo to investigate spirals
This is the second in a twelve part introduction to Logo for beginners. In this part you learn to draw polygons.
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 use LOGO to create a systematic reproduction of a basic
design? An introduction to variables in a familiar setting.
Using LOGO, can you construct elegant procedures that will draw
this family of 'floor coverings'?
Learn about Pen Up and Pen Down in Logo
Turn through bigger angles and draw stars with Logo.
Write a Logo program, putting in variables, and see the effect when you change the variables.
Logo helps us to understand gradients of lines and why Muggles Magic is not magic but mathematics. See the problem Muggles magic.
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. . . .
More Logo for beginners. Now learn more about the REPEAT command.