Spleenwort Fern

I changed a sign or few in the matrix transforms. I think this is what Barnsley and Wagon intended people to get when implementing their model. This is way cooler looking too.

This is a fractal representation of a Spleenwort Fern. It is infinitely complex in that no matter the magnification, the resolution does not change. Essentially the fern pattern is what makes up every fern you see. Enjoy.

Sand Dollar Success!

I figured out what was wrong with my program.  There were two things:

1.  I needed to use the output as the new input, instead of sending a set of predetermined points through the function to generate output.

2.  I was taking the square root of a number that didn't need it.

In the end, the fixes took a grand total of a minute to fix in the program; however, it took many hours to discover what was wrong.

Enjoy my sand dollar.

My MS degree exam questions

1.  Explain the Schodinger's cat paradox.

2.  Consider the Stern-Gerlach (SG) experiment.  If you direct a beam of ions through one SG apparatus, and then place another SG apparatus oriented the same as the first in the path of one of the first split beams, then place a screen on just beyond the second SG apparatus, how will the ions be distributed on the screen?  Follow-up:  how many ions should hit the screen given a beam containing 1000 ions.

3.  A sailor drops a ball from the top of the mast on a sailing ship.  Where will the ball land?

4.  Consider a rod of uniform mass density resting balanced on a cylinder when a puff of wind tilts the rod.  At what angle will the rod slide off of the cylinder?  Note: there is static friction between the rod and cylinder.  Follow-up:  is the rod stable if it tilts by small angles compared with the angle required to slide off?  Follow-up:  will the rod experience harmonic motion at the small tilt angles?

5.  What makes the dynamics of neurons nonlinear?

Do YOU know the answers?  

statistically unique solutions

Is there a mathematical model which statistically predicts a more likely solution over another?  Often times in "real world" physical problems, there is no unique function or solution to determine the evolution of a system.  This occurs in many other sciences and applications.  So, I'm wondering if a statisical prediction of which solutions might work can be found.  In some simple systems, like the kinematic equations for constant acceleration, there are an infinite set of solutions how an object behaves under the influence of a constant acceleration.  All one needs to do to solve the problem is to pick a set of initial conditions for the position and velocity of that object.  However, in some problems like building a three-dimensional image of a brain from magnetoencephalography (MEG), there is no unique image based on the data gathered from the MEG probes.  But there must be some way in which one can determine the most likely image of the many (if not infinite) options...right?