Fractal Geometry and Landscaping.

[White Gardens]

So the other night I watched an interesting NOVA special. It had to do with fractal geometry.

I can't explain it well, but this might. If you've got the time you should watch the full episode. Highly enlightening.

http://www.pbs.org/wgbh/nova/fractals/set.html

In the episode, they used fractal geometry to estimate the amount of CO2 a rain forest can absorb. Astonishingly they figured it to be an easy fractal equation.

Fractal geometry can be used for an infinite number of things in the natural world such as estimating coast-line miles, and how the human heart beats with a fractal rhythm.

My question is, can there be a way to incorporate fractals into Landscape design. ???

Any thoughts.

[Runner]

Probably as far as turf grass reproduction. :) Other than that, what...ground covers?
You want to see a good example of this,...look at some of the resort islands they are building over in Dubai. I'm not sure if they are exactly fractal or not, as some of them are surrounded by loops, but it's much like that.
http://images.google.com/images?q=man+made+islands+of+dubai&oe=utf-8&rls=org.mozilla:en-US:official&client=firefox-a&um=1&ie=UTF-8&ei=JxCQSqK3LY3sMdXu_a8K&sa=X&oi=image_result_group&ct=title&resnum=5

[White Gardens]

That's a fairly good example Runner.

Fractal or not in the man made islands of Dubai, the idea behind fractals is that there is a mathematical equation that explains everything that we perceive to be erratic. Examples being mountain ranges, coast lines, plant forms, etc....

So, such in the case of Dubai, it might be inadvertently a fractal equation.

When thinking about landscaping, there are certain principals to observe. One being for example, start your plants lower in the center of the structure, build height to the edge of the structure, and then have your tallest plant (tree) away from the structure. So what you achieve is a visual step from the center out.

Some Fractals show up on graphs in line form similar to radio signals, a peak and valley type of graph.

I'm wondering if you could find a plotted fractal that would be visually "perfect" to place in front of a structure, and then all you would have to do is fill in your plants in the hills and valleys of the plot.

Even if you were to find an equation to fit, you would still need to be able to plug in the proportion of the structure or area you are trying to fill.

I know, it's out there, but sometimes I like to think.:hammerhead:

[PaperCutter]

Mathematics is funny. Look at the golden mean- you really can get a pleasing set of proportions using it. J.S. Bach's music has been analyzed, and determined to be so mathematically perfect as to lend credence to those who would say it's divinely inspired. So, fractals? Why not? For me, it would have to be a Winter Project- I could never find time to mess with that in season.

Check this out: http://www.michelesaee.com/content/projects/continuing/shakespearean_theater/project.pdf

The idea was a re-imagining of the Globe Theater. The architect proposed putting sensors on the actors (like they do when live movements are being converted to CG), graphing the movements of them performing scenes from Shakespeare, and converting that information into a 3D space to form the shell of the theater. I saw the exhibit in the National Building Museum, and it was pretty awesome. It's not fractals, but if you like far-out design concepts, it's out there.

[Cloud9Landscapes]

It's all greek to me.

[Roger]

In a former life, I worked extensively with contours. These were not land contours, but rather contours of some equal value (e.g. temperature, deflection, magnetic fields, stress, flow, etc). Working with contours was important to determine the validity of answers, not necessarily the exact values, but rather patterns or flows.

Also, in another life I did work to some extent with land terrain, hence lines of equal height. That was necessary to understand water flow, drainage, etc.

Now, at times I realize that I visualize the ground in terms of contours and how they would run. I get a mental image of lines of constant elevation. The image helps me understand where to run my mowers for least resistance. Also, trying to visualize the contours' separation provides some measure of slope -- closer contours, steeper slope.

I also know that when trimming bushes, I mentally work out the equations for the surface of the bush. Obviously, these shapes are in terms of R, Z, and Theta. The ideal is to find the equation of all surface points to provide constant R, for all values of Theta, at a given Z. In other words, the function to describe the final shape of the bush is in terms of R, T, and Z, with R being the dependent variable, the Z being the independent variable. I don't work enough with spherical shapes to work in terms of R, Theta, and Phi. Keeping the function in mind sure makes trimming many bushes more challenging and interesting than just "trim 'er down."

I suppose I do this subconsciously more often than I might think. I guess it reflects much time spent with the concept lines of equal value.

I know, not quite the same the idea being discussed for fractals. My mind can only process three dimensions, and the equations associated with the X,Y,Z (or R, T, Z, or R, T, P) ahead of me.

[White Gardens]

Dang Roger, and I thought I was an over-thinker.:hammerhead: Great Equations you've got there.

All good points. I might just have to wait till the winter and go talk to a Math professor at the local College and see what I come up with.