Fractals; Complexities & Nature

[Adam Clayman]

 Mandelbrot sets are the mathematical basis for the randomness found in nature. Craggy edged bug-like structures, associates everything, even GCA, to nature's infinite complexities.

These random structures are also infinitely fascinating because they are based on simple formulas. F=f(squared)+c

Is the secret to building quality golf courses a simple formula?

[Mark_Rowlinson]

Adam, I am only responding because I hate to see posts unanswered.  Unfortunately I haven't a clue what you are talking about, so I'll go back to my arithmetic primer.  Now, where was I?  Of course!  3+6=?

[Brad Tufts]

It seems to me that the simplest way to design and plan a quality golf course is to use the lay of the land.

I would assume if you had to create an environment or landscape before desiging or building, this would make a project much more complex.

Also, what results from the simple lay-of-the-land golf course is the complexity of nature, the bounces and quirks and micro-environments.  This is preferable to the often too-fair and manufactured course design resulting from a manufactured setting.

I think your comparison is apt.

[Adam Clayman]

Mark,
It's free day here at the asylum.

I'm trying to inspire thought on the randomness of nature and how easily quantifiable it is, using simple formulas.

Do those who design and build courses, find this is also to be true?


Thanx Peter, Sets.

 Brad, Daft is what I expected. I'm trying to think through the differences betweend difficult and complex.

[Mark_Rowlinson]

Peter, Thank you for clearing that up!  Back to the primer again.   As you clearly know so much about this, would you just slip me the answer to my arithmetic problem?  I'm still struggling with it.

[Garland Bayley]

...
I'm trying to inspire thought on the randomness of nature and how easily quantifiable it is, using simple formulas.
...

I believe that fractal geometry is not an exercise in randomness. Instead it is an exercise in repeatable patterns as decribed in the formulas.

Landforms are different as they are somewhat random since they are carved by more random phenom. such as wind and rain.

[Steve Burrows]

If I may, I'd like to recommend a book on this subject.  It's called "Biomimicry," by a scientist (I couldn't tell you what specific discipline, but somewhere in the life sciences) named Janine Benyus.

She argues that the built environment could be better designed if we absorbed everyday lessons (such as the strength and simplicity of a spider's web) from the natural world and applied them to our designs.

So, perhaps golf, and golf course design, is cannot be summed up in an equation, but surely we can all benefit from the sometimes subtle education of the natural environment.

[Jay Flemma]

I thought - and I may be way off - that fractals had something to do with chaos theory in mathematics?  You know, like storm formation and ocean wave patterns and what happens when you mix dinosaurs and humans (sorry thats a Jurassic Park joke for all you that missed the reference...)

Would that not inject events far to random to be reliable?

[JohnV]

To quote from Wikipedia, "a fractal is a shape that is recursively constructed or self-similar, that is, a shape that appears similar at all scales of magnification and is therefore often referred to as "infinitely complex."

Drawing Mandelbrot sets were something that we used at Sequent Computers to show how parallel computing could improve performance back in the 1980s.  It was pretty cool and worked well because each location in the set was independent of the others around it.

Nature can be looked at this way.  It is possible to take a set of pictures of some natural object at different levels an be unable to tell which is which.  For example, a picture of a coast line from above looks the similar in terms of the land mass to water border regardless of whether it was taken from the space shuttle or at a high level of magnification.

Some fractals functions are random and some are not.

Notice how by applying some random functions to a simple triangle and permutating it you can get something that looks like a mountain range.

[Kirk Gill]

There's not a lot of randomness in golf course architecture. The structured quality of the game combined with historical traditions that dictate many of the parameters of the golf course don't leave a lot of room for random chance.

But this question makes me think of a particular jazz album I've always loved called "Mingus Ah Um" by Charles Mingus. What Mingus was doing at this point was writing music that left space within it for improvisation. Not just during the solos, but during the orchestrated sections of the pieces there were times when each particular instrument's part was left blank, open to the interpretation of the musician, or sometimes more than one musician at a time. Within the structure of the written music existed space for the individual to improvise a part that they felt complimented the structure. It introduced an element of more than randomness - instead an element of skill combined with inspiration.

In a way, the golf course architect is like one of those musicians. The land itself combines with the rules and traditions of the game to provide the structure within which the architect and the builders use their skill and inspiration to provide a design that exists harmoniously.............

Am I making sense?

[Bill Gayne]

Adam,

I really feel that you're on to some cutting edge thought here. However, for this to be validated it requires Tom Macwood and Tom Paul to reconcile the arts and craft movement with the fractal school of design. At present these thoughts are causing grave concern and internal conflict. The explanations of fractals are making the writings of Max Behr seem rather simplistic and easily understood.

Tom Doak should have stayed at MIT if it's about fractals.

[Tom_Doak]

I don't think it's about fractals, but one of my associates has a degree in mathematics, so I'll ask her if there is any comparison.

However, I could relate to what Kirk Gill was saying, with one additional thought -- the architect is the composer of the piece, but the golfers are the players.  We think we have set up the basic script for the golfers to follow, but often their bodies decide to improvise and find a new route -- and on the best-designed golf courses, their improvisations still work out to be music instead of noise.

[Ted Kramer]

Adam,

I really feel that you're on to some cutting edge thought here. However, for this to be validated it requires Tom Macwood and Tom Paul to reconcile the arts and craft movement with the fractal school of design. At present these thoughts are causing grave concern and internal conflict. The explanations of fractals are making the writings of Max Behr seem rather simplistic and easily understood.

Tom Doak should have stayed at MIT if it's about fractals.

That made me laugh out loud.

-Ted

[Dan Kelly]

Adam,

I really feel that you're on to some cutting edge thought here. However, for this to be validated it requires Tom Macwood and Tom Paul to reconcile the arts and craft movement with the fractal school of design. At present these thoughts are causing grave concern and internal conflict. The explanations of fractals are making the writings of Max Behr seem rather simplistic and easily understood.

Tom Doak should have stayed at MIT if it's about fractals.

As we white, nerdy guys say: LOL!

It just can't be a coincidence that I read (sort of) this thread just before I came across this: http://www.youtube.com/watch?v=-xEzGIuY7kw

[Tim Bert]

Nice video!  I didn't realize that Weird Al was still hard at work.

[Steve Lang]

 

Mudder,

What if 6.. turned out to be 9?  I don't mind.  I don't mind.  

Amorphous silicon will probably dominate materials of construction for solar collectors.. but like fractals, are only a form and must be put into shape and organizational purpose by human (e.g. gca) thought..

No eliminating the middle man and woman in the gca endeavor, lest one wishes to have no deviation from the past.

[Adam Clayman]

JVB, Touches on the aspects that mimic nature. Slight alterations in the sequence, or position, and we get the randomness we see when we look at a grove of trees. Or a FLW repeated detail. Same pattern(set) only randomly placed.

Seve, I always thought 7 ate nine.

Who can guess the course I thought of when I first saw the tributaries of the Mandelbrot set? Hint; It's not open yet.

[Ron Farris]

Adam,
While working with Dye in Japan the engineers explained to us the degree which one could build a bunker slope in a particular soil.  I told them that we should build it according to the Dye style.  He said that it would simply fall down during the rainy season when the soil became saturated with rain water.  He also proceeded to show me his calculation if such a slope existed and they were hit with a mild earthquake.
It made my head spin like the Exorcist movie.  We decide to build it in the Dye style with steep grass faces.  Conclusion was that if it fell down then they would simply rebuild it in the Dye style.  

I haven't been back to see if it held.  However, I do remember Perry having another project utilize utility poles stacked on top of each other to help stabilize it.  I imagine that one has met with trouble.

[Tom Dunne]

This thread is cool. Triggers a lot of associations that I'm not entirely sure how to sort through, like ferns and spirals and the "turtle" from that old '80s computer program freaking out and scribbling lines for five minutes on the screen.

And quotes like:

Big fleas have little fleas
On their backs to bite them
and little fleas have littler fleas
and so ad infinitum

--Swift

and:

There's no question that we as architects can simply never be as creative as Mother Nature. We can't produce the randomness, the amazing variety of contours, or the way that vegetation inhabits a landscape. But we can study nature and follow its lead. (itals mine)

--Bill Coore