Bubble sort is the first sorting algorithm that you learn in many algorithm classes. It's not a particularly fast technique, so it's never really used in practice. And generally if you're writing your own sorting algorithm instead of relying on one that your platform provides th…

The Dragon Curve or Dragon Fractal is a nifty little shape! Here are the first 12 iterations. You see the dragon shape begin to emerge. I've put a red dot before each one, so you can see how it doesn't always go forward right away. ;export dragon to dragon :count :length :angle…

A simple self-similar fractal. Similar to a Tree -- in particular it's very similar to the Pine, but with a tilt before drawing the next segment. to fern :segment :curve :angle1 :angle2 :ratiobranch :ratiostem :limit penwidth :segment/4 ifelse :segment>:limit [ color [60 40 20…

The flowsnake, also known as the 'Peano-Gosper' curve is a rather dashing space-filling curve. There is also a demonstration of it on the space-filling curves page. The following implementation uses 'mutual recursion' - i.e. two methods that call each other. The flowsnake has the…

Few spirals are as beautiful as the Harriss spiral. to curve :length pu lt 45 fd :length/2 * sqrt(2) rt 90 pd penwidth :length/15 arc :length/2 * sqrt(2) 90 pu fd :length/2 * sqrt(2) lt 90 lt 45 rt 90 pd end to harriss :length :limit if :length > :limit [ color [200…

Perhaps the best known Space Filling Curve is the Hilbert Curve. to hilbert :count :size :angle if :count > 0 [ rt 90*:angle hilbert (:count - 1) :size (:angle * (0-1) ) fd :size rt 90*:angle * (0-1) hilbert (:count - 1) :size :angle fd :size hilbert (:count - 1) :size :…

A Koch curve is a well-known fractal, first described by a Swedish Mathematician, Helge Von Koch, in his paper "Sur une courbe continue sans tangente, obtenue par une construction géométrique élémentaire". Put three Koch curves together in a triangular configuration and you have…

In the article on Koch Curves we derived the famous koch-curve, by starting with a line, then a bumpy-line, then a self-similar recursive bumpy-line. The final result looked like this: to koch_curve :length :limit ifelse :limit = 0 [ fw :length ] [ koch_curve :length/3 :limit -…

A famous non-repeating tiling pattern, invented (discovered.) by Roger Penrose, a giant in the worlds of mathematics and floor-coverings. The following logo program produces a penrose tiling. I found this at http://logo.twentygototen.org/E3_yJcQ4. I haven't looked through it en…

"Mr Escher's office please" "Up the stairs, keep turning right" —@MooseAllain In Real Life Cartoon —New Yorker Cartoon By Robert Leighton Logo Version to piece :size lt 60 fd :size lt 120 fd (3* :size) lt 120 fd (4 * :size) lt 60 fd (1* :size) lt 120 fd (3* :size)…

I remember a maths teacher saying to me, "It's amazing how clear it is, when you use Logo, that a circle is just a polygon with an infinite amount of sides" In that spirit, here's a simple formula for a polygon. Repeat {sides}: Forward {length}, Right Turn 360/{sides}. I tried …

Ever wanted to drill a square-hole? Is it possible to build a drillbit that would produce such a shape? It seems impossible, but how impossible is it? Can we drill holes that are any shape other than circular? A circle is a curve of constant width. As you rotate a circle its wi…

Sierpinski didn't just mess around with triangles, he also wrote 50 books (all of them flip-books of Sierpinski triangles, I assume), created a curve and finally — the highlight of his storied career — he released this: his Sierpinski Signature Edition Carpet design. A short warn…

to half_sierpinski :size :level ifelse :level = 0 [ forward :size ] [ half_sierpinski :size :level - 1 left 45 forward :size * sqrt 2 left 45 half_sierpinski :size :level - 1 right 90 forward :size right 90 half_sierpinski :size :level - 1 left 45 forward :size * …

A Sierpinski triangle is the result of this line of thinking: To draw a Sierpinski triangle just draw three smaller Sierpinski triangles. (Unless the shape is too small... then just draw a regular triangle). What if we make the number 3 a parameter, :side, so that we create Sie…

Anything that's covered here is almost definitely covered in a very well known webpage, The Sierspinski Triangle Page to End Most Sierspinski Triangle Pages but regardless, I must press on. Let's draw a triangle. to triangle :length fd :length lt 120 fd :length lt 120 f…

Space-filling curves! Amazing things. Peano sat around thinking and thinking, What was he thinking? He was thinking: I wonder, I wonder, I wonder! Can I draw a continuous line that touches every single point of the unit square, exactly once? (i.e. it never crosses itself!) No…

Swirls and spirals appear in nature in all kinds of places. In the seeds of a sunflower, in the vortex of a hurricane, in the horns of a goat, in the shell of a snail, in the curling fronds of a fern, in this guy's beard. . In this totally naturally occurring jetty: Spirals in…

A simple self-similar fractal. Similar to a Fern Here's one that bifurcates at every iteration. By altering the angle of the branches we get completely different shapes. Topologically identical, but visually very different. ;export tree to tree :length :branches :angle :ratio …

I wanted to draw a triangle, so I sat down on the ground and thought about it for a while. When it all comes down to it. What it is, you see. How it works. Well a triangle has. It has 3. - 3 points. - 3 corners. - 3 angles. It's 3 lines really. So I want to draw 3 lines. The …