Author: John Winkelman

Lindenmayer Systems and Generative Art

John Winkelman

lindenmayer-1

This is a Lindenmayer System pattern with the grammar “+F!F-[F+F]-[F-F]!”. Confused? Click here to create your own.

A Lindenmayer System is a formal grammar used to generate rule sets for describing the phenotypes of algorithmically created plant analogs.

There. That should have scared away the lightweights.

The thing sitting above this block of text is a Lindenmayer System explorer. It is used to turn blocks of text into procedurally generated patterns which resemble plants. This system of generating graphics is so successful that it is used in many, if not most, of the current popular games to create plants in-game, on the fly, so users donÃ’t need to install hundreds of megabytes of graphic textures.

Tool Description

Line Length – length of a line segment, in pixels.

Line Scalar – percentage by which the line length will shrink, in each succeeding iteration. “1” means the line length will not change. Between 0 and 1 means it will shrink. Greater than 1 means it will increase in length.

Line Width – Width of a line segment, in pixels.

Line Taper – percentage by which the line width will shrink, in each succeeding iteration. “1” means the line width will not change. Between 0 and 1 means it will shrink. Greater than 1 means it will increase in width.

Line Color – the color of the line segment, expressed in Hexadecimal RGB format. 000000 is black. ffffff is white. Use a comma-delimited list to display different colors in succeeding iterations; for example, “000000,333333,666666,999999,cccccc” (without the quotes) for gradually lighter shades of gray.

Angle – Degrees in which the angle of the next iteration lines will differ from the current.

Angle Taper – Alters the degree of branch offsets. Not currently used in this tool.

Iteration – Number of times the rule set is recursively built out from the initial grammar. Any number greater than 1. With complex grammars, more than 5 tends to bog down the system as the rule set is generated.

Axiom – Initial seed from which the grammar is built. Currently only the character “F” is used

Grammar – The rule set which describes the pattern which will be created using all of the preceding settings. The genotype, if you will. Always starts with “F”

Allowable Characters in the Grammar set, and what they do

F – draw a line segment
+ – increase the drawing angle
– – decrease the drawing angle
[ – start a branch
] – end a branch
! – reverse the angles of the current rule set

Here are some combinations of presets and grammars which create interesting patterns:

The pattern on the front page which enticed you to play with the L-system explorer:
Grammar: F:+F!F-[F+F]-[F-F]!
Angle: 15
Iterations: 4

Hexagon tessellation pattern:
Grammar: F:F+F-F+F-F-F-
Angle: 60
Iterations: 4

Generic vine:
Grammar: F:[F+F]F[F-[F-F]F]F++[F+F]!F
Line length: 10
Angle: 25
Iterations: 3

A shrub-ish thing
Line length: 20
line scalar: .9
line width: 10
line taper: .9
line color: 331100,663300,994500,cc3300,ff9933,00ff00,ff0000
angle: 10
iterations: 3
grammar: F:[F[F+F]![F+F]]-F-[F-[F]F+F[F+]-]!F

Have fun, and if you come up with something especially interesting post it in the comments!

What I’ve Been Thinking: The Economy

John Winkelman

I spent a good chunk of my time this past year trying to get a handle on just what, exactly, had happened to the world economy, and how it had happened. I am absolutely not an economist, so most of what I heard made little sense. However, the parts that I did understand either made me furious, sad or scared. Seems that all of the “fixes” which have helped the economy “recover” are just band-aids, and have not fixed the fundamental problem, which is that, on the personal, local, national and global level, we are spending more money than actually exists, and the only way to prevent this whole edifice from collapsing is to continually spend more money. I realize this is an incredibly over-simplified view of the issue, but nothing which I have read has in any way contradicted it.

Two websites have been quite helpful in my research: Barry Ritholz’ The Big Picture and Naked Capitalism. Each publishes several articles a day, and do a good job of digging through the corporate/political smokescreens to get at the actual numbers.

Round about election time, I came across an online Federal budget simulator which allows users to sort out the Federal budget, with an eye toward “Stabilizing the U.S. Debt at 60% of GDP by 2018″. In other words, keep the debt from eating us. I ran through it a few times, and let me tell ya, it isn’t easy. In fact, it is impossible without making changes, increases, and cuts which would leave everyone’s oxen pretty well gored. The plus side is that the industries which lobby the hardest to get laws changed in their favor would be the hardest hit. I will post my solution in a future update. I will tell you that, among other things, I would not be eligible for social security until I was around 70, which is fine with me.

If I were the benevolent overlord of the world, one of my first commandments would be “Thou shall not make a profit in a manner which damages the system which allowed you to make that profit”.