However, I have not lost hope.  Someone may still find the box and call me for the $30 reward.  Here are some pictures from the project as it developed:

This project is almost identical to the one found described on this site, and theirs worked:

http://space.1337arts.com/

Equipment:

Software:  All of it was free!

Advice:

1.  The phone with instamapper is a really inexpensive GPS tracker.  However, it only works in areas with cellphone coverage.  Therefore, you won’ t be able to track most of the flight (no coverage above 7000 feet) and the balloon has to land in an area with coverage if you ever want to find it again.  It can really limit your possibilities depending on where you live.  If I had to do it over again, I would buy an actual GPS tracker, which can function virtually anywhere at any height.

2.  I paid way too much money for the parachute.  Go to your local hobby shop and get a big rocket parachute instead.  They’re only about $15.  Probably less.

3.  When you are filling the balloon, make sure you have it underneath a weighted down tarp or tent canvas or something like that.  My first balloon escaped me before I had anything attached; a costly mistake!

Videos that inspired me:

Edge of Space I:

Stratos I

More on this later.  Feel free to ask any questions that you may have about specific details.  I know that I had a lot when started the project.

Don’t ask.

I really like the idea of creating organic shapes, and one of the best ways to do that is to have your script generate hundreds of random points and then to use them in whatever way you think of.

I also milled a face out of foam:

I didn’t actually draw the face myself.  I found it on Google 3D Warehouse at this link:

http://sketchup.google.com/3dwarehouse/details?mid=42067fdd5130ebcaf9e5286b0eab37fe&prevstart=24

Apparently, it was produced by a user called moon, so I give the drawing credit to him.  I just made the milling path for the CNC machine that we have.

I like to think of this as a sort of promotional material.  This cube could be mass produced and distributed as advertising for the class.  You could give it to someone and say:  “Come to All Hands on Deck.  We make cool stuff like this!”

Here are some pictures of the work in progress:

And then lofting those geometries.  Using the record history function, I could move the geometry and the loft would update accordingly.  I came up with these shapes.

We were taught how to use the surface sculpting function of rhinocam in order to cut these shapes out using the CNC machine.  I didn’t get around to making the toolpath for my surface though.

However I did work more on my bowl.  I laid out all the pieces flat.

And then spent a while figuring out how to make the toolpath for theses parts.

In the end, rhinocam produced the g-code, which is basically a long list of coordinates that outline the path the CNC drill bit has to take in order to cut out my parts.

The actual script can be copied and pasted from the word document below into the Rhinoscript editor:

Mandelbrot.doc

So how does it work?

The Mandelbrot fractal works on the basis of this function:

Z = Z² + C

Now the variables Z and C represent complex numbers.  The reason that Z is on both sides of the equation is that the resulting Z value can be put back into the equation in an infinite loop.  A complex number is the combination of a real and an imaginary number such as 1 + 2i where i is the square root of -1.  An imaginary number can also be expressed as a coordinate such as (1, 2).  Complex numbers can be added together or multiplied or squared just like integers.

For instance, if you wanted to add (1, 2) and (3, 4), you would go about it this way:

1 + 2i + 3 + 4i = 4 + 6i

or (4, 6)

If you wanted to multiply the two coordinates:

(1 + 2i) ( 3 + 4i) = 3 +6i – 8 = -5 + 6i

or (-5, 6)

Testing a point

With that explained, the rest is pretty simple.  The Mandelbrot set is just a test of points.  You can test any point in the x-y coordinate plane using the afore-mentioned function and what you will find out is that that point is either in the mandelbrot set or it isn’t.

Say you want to test to point (-1, 0); you will use this complex number as your C value and Z will start out as (0, 0). So,

Z = (0, 0)² + (-1, 0) = (-1, 0)

Now you have just calculated the first iteration of that point.  (-1, 0) is now your new Z value.  For the next iteration you just feed this value back into the equation (the C value never changes, it is always your original point):

Z = (-1, 0)² + (-1, 0) = (0, 0)

Then you can plug this value back in:

Z = (0, 0)² + (-1, 0) = (-1, 0)

As you continue to run iterations on a point, one of two things will happen.  Either the point will eventually move away from the origin into inifinity, or it will never do so.  The points that move away into infinity are called the escape set.  The points that are effectively trapped in an area around the origin are called the prisoner set or the Mandelbrot set.  In the image above, the points shown are those that are in the M-set.

Of course it would take a person months to run 20 iterations on each point in a set of 10,000 points.  That is why, using the principles above, I had a computer do it for me.

So that is how the Mandelbrot set works.

My original bowl shape just didn’t work for making notches.  The walls were too thin.

So I started over with a new shape.  I kind of created a system for getting the notches by using rings that were half the width of the actual stacked rings.  I ended up with this:

You start out with just one line like so:

Then you rotate a copy of the line 90 degrees counter clockwise, using the top of the line as your center of rotation:

Then, you rotate a copy of the two lines 90 degrees counter clockwise, using the end of your most recent line as the center of rotation:

Then you continue rotating a copy of your entire shape using the newest end as your rotation point.

Eventually you will end up with something like this.