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= Logo = | = Logo = | ||
Revision as of 14:38, 10 September 2007
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Logo
Logo was developed in the 1960's originally as a text manipulation language. The use of it for graphics was initiated by Seymour Papert who developed the Turtle graphics extension for which Logo is now famous. Papert's main motivation was to build a simple system that would encourage children to learn programming, and although simple, Logo is a full language, with support for functional programming, file access and other IO.
Logo is often taught in schools and educational institutions as an introduction to programming. The idea behind Turtle graphics is a very physical one, and is often implemented in terms of controlling a robot.
A turtle can be imagined (or often built) as a floor roving robot with a pen positioned in its base. The pen can be raised or lowered to enable it to draw lines on the floor. In advanced implementations the pen can be swapped to change the colour of the line, but many see this as an unneccasary frivolity.
The basic turtle commands are very simple, and the following code will draw a square:
FORWARD 100 LEFT 90 FORWARD 100 LEFT 90 FORWARD 100 LEFT 90 FORWARD 100
Also the commands for controlling the pen, PENUP and PENDOWN. The following code will draw a dashed line:
FORWARD 10 PENUP FORWARD 10 PENDOWN FORWARD 10 PENUP FORWARD 10 PENDOWN FORWARD 10
Like any other language, Logo has support for looping, this command will draw a circle (as 360 lines):
REPEAT 360 [FORWARD 1 LEFT 1]
To make a procedure:
TO SQUARE REPEAT 4 [FORWARD 10 RIGHT 90] END
With arguments:
TO SQUARE :size REPEAT 4 [FORWARD :size RIGHT 90] END
The thing is that Logo was often written live, in a command interpreter, and being a functional programming language (technically a variant of the lisp family) it's not very long until you start writing recursive graphics functions. This snippet draws a spiral:
TO SPIRAL :length IF :length > 30 [STOP] ; have to end when the lines get too long FORWARD :length RIGHT 15 ; draw a line, and turn a bit SPIRAL :length *1.02 ; call ourself again, making the line a bit longer END SPIRAL 10
http://www.pawfal.org/nebogeo/images/spiral.png
A spiral.
Where is this all heading?
Well, recursive graphics are an elegant way of getting complex results from a bare minimum of code. In very few lines it's possible to draw a huge amount of fractal like complexity. This is obviously a good thing for an artist wishing to try live coding - a few minor changes to the code can result in big changes, so much so, that it often feels like cheating.
TO TREE :distance IF :distance < 5 [STOP] FORWARD :distance RIGHT 30 TREE :distance-10 LEFT 60 TREE :distance-10 RIGHT 30 BACK :distance END TREE 80
http://www.pawfal.org/nebogeo/images/tree.png"
A tree.
Scheme
I mentioned earlier on that Logo was a variant of Lisp, well another (closer one) is Scheme. Here is the spiral program rewritten in scheme:
(define (spiral distance)
(forward distance) (right 15)
(if (> distance 30)
1
(spiral (* distance 1.02))))
Scheme is a tiny, simple language. Like logo, scheme is often used as a teaching tool, for it's elegance and simplicity. People often use it to learn about programming languages, and as an extension scripting language for applications like the gimp. I wouldn't really like to write huge applications natively in scheme, but it has its merits as a live programming language, as you can get a lot done per line of code.
The prefix style--doing arithmetic like (* 4 5) where the operator goes first--seems confusing to begin with, but it actually makes the language a lot simpler as all function calls are the same. It's really easy to do recursion (actually, it's the only way of looping in Scheme), and also you can easily write scheme programs that edit and parse other scheme programs, but I haven't investigated this too much yet.
My first livecoding graphics environment was just a hacked version of a scheme example which implemented turtle graphics in a window. I changed the program to execute its scheme script every frame in a loop, so you could change stuff live.
Fluxus
Fluxus is a 3D rendering environment, a smaller version of the renderers you get in a game engine such as Unreal or Quake. It's also got a few extra features that game engines do not usually have, firstly it can capture audio input, and process the audio to extract the harmonic content of the sound. Secondly it is entirely driven by a realtime scheme script editor - for live coding.
As fluxus produces 3D objects, rather than lines - the graphics code is a little more complicated than the turtle graphics we've already seen. Fluxus uses a common method used in graphics, based on the OpenGL library that it uses, the state machine.
Lets have a look at some fluxus code:
(colour (vector 1 0 0)) (draw_cube) (colour (vector 0 1 0)) (draw_cube)
This fragment of script will draw a red cube and then a green cube. As the state of the colour state is changed, it effects the commands passed after it.
These states can also be stacked, using push and pop commands - which means to take a copy of the current state so you can change it and then pop it back to how it was before:
(colour (vector 1 0 0)) (push) (colour (vector 0 1 0)) (draw_cube) (pop) (draw_cube)
This will set the colour to red, then push the state, and draw a green cube. The pop then sets the state back to how it was before the push, and will then draw a red cube. I sometimes indent pushed state code like that to make it easier to read.
There are a few items that you can modify on the fluxus state machine - one of the most important is the transform state. This allows you to translate, rotate and scale objects, and follows the same rules as the colour state. As with Logo (where the state was just as important, but was implicit in the postion and orientation of the turtle) manipulating the state is handy for recursive modelling.
(define (tree d)
(push)
(rotate (vector 0 30 0)) ; twist the branch
(translate (vector 0 0.4 0)) ; move up a bit
(scale (vector 0.8 0.8 0.8)) ; shrink so branches get smaller
(push)
(scale (vector 0.1 0.6 0.1)) ; make the cube thinner and more branch like
(draw_cube) ; this is our cube
(pop)
(if (eq? 0 d)
1
(begin (rotate (vector 0 0 45))
(tree (- d 1)) ; one subtree branch
(rotate (vector 0 0 -90))
(tree (- d 1)))) ; another subtree branch
(pop))
(colour (vector 1 1 1)) ; set current colour to white
(every-frame "(tree 10)") ; draw the tree every frame
http://www.pawfal.org/nebogeo/images/tree2.png
Another tree.
Live programming with fluxus
The audio input features combined with the same recursive graphics that come all the way from the days of Logo allow the live programmer to quickly make complex shapes that dance to sound (of course it works better if that sound is live coded too). I've found the best way to "play" fluxus in this way is to rig up a template recursive function that you can work on throughout a performance - adding new modifications and recursion depths as you see fit.
There is more to fluxus than recursion though. There are features allowing you to employ physics animation to your scene, so objects can fall, bounce off each other or be kicked around to the music. Also there is a full flocking system for boid like behaviours. One of the newest additions is a turtle style polygon modeller, so you can use a turtle to draw polygons and join them together into 3D shapes.
Links:
- http://www.papert.org/
- http://el.media.mit.edu/logo-foundation/
- http://swiki.hfbk-hamburg.de:8888/MusicTechnology/284
- http://www.swiss.ai.mit.edu/projects/scheme/
- http://www.schemers.org/
- http://www.pawfal.org/Software/fluxus/
- http://www.red3d.com/cwr/boids/
- http://www.gimp.org/
- L-Systems in SuperCollider
The logo figures in this document were produced with the Berkeley Logo distribution which can be downloaded from here: http://www.cs.berkeley.edu/~bh/logo.html