Sand Dollar Success!

I apparently wrote this back at the end of May, but never uploaded it here...

 

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 shouldn't

Morphospace

Consider a space in which two traits are mapped in a plane.  These two traits could be any description of an organism.  In an environment certain combinations of the traits will allow an organism to make better use of the environments resources.  Now consider a resource landscape mapped onto the same plane as the trait space.  Trait coordinates on areas of higher points in the resource landscape correspond to the ability of those organisms in the area being better able to reproduce, because they are better at using the resources given by the environment.  These areas may allow the organisms to have more offspring.  Lower areas in the landscape mean that the trait coordinates over the area are less apt to reproduce, because the resources in the environment are not as well suited for those organisms.  These areas reduce the chance the organisms have to reproduce, thus birth rates can be lower.

Each organism has associated with them, a mutation parameter we call 'birth noise'.  The birth noise of an organism determines an area around it and it's mate (mates are chosen as the nearest neighbor in trait space) in the trait space in which their offspring may appear.  This is to model the variation in traits of offspring from their parents.  The birth noise of the choosing parent then passes it's birth noise on to the offspring, modeling the inheritance of genetic information.

 

There's more about death and other details, but I needed to attempt to describe these two topics.
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Adam D Scott

Student Answers Exp 5 1012

Q:  Explain how the earth's magnetic field could affect your results when measuring magnetic field directions around a DC wire.  Based only on your data, can you tell what side of the laboratory is facing (magnetic) north?

 

"The earth's magnetic field could possibly interfere with the needle of the compose by detecting the magnetic field produced from the current in the wire to the magnetic field that indicates north on earth.
The direction of the compass and the magnetic field of the earth is pointing to the back of the lab toward the door by the magnetic field earth actin on the  force this is the result of the sum of the vectors from the earth."

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Adam D Scott

Student answers: Exp 6 1012

"Since the equation ... decreases as the capacitor increases, we know that the current will be less for the larger capacitor."
First of all, equations don't change; values in them may.  Capacitors don't change in the experiment they did; the charge stored on the capacitor is what changes.  The current only decreases at a slower rate for a larger capacitor; it's initial and final value has no bearing on what capacitor one uses, though.

"Another error is due to the fact that the timer is pretty quick and we are either getting the measurement a bit too early or a bit too late..."

Makes timers counting off seconds are too fast...but they count seconds, so seconds must be too fast...so life is too short?

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Adam D Scott

More on Logistic Map

Here are several "slices" of the output vs. time from the orbit diagram. They show the output as it changes from iteration to iteration (time). The plot title is the corresponding r value, so you can compare how many different "lines" there are going across each plot (after about midway through the x-axis), to the number of points for each r value in the orbit diagram. It may be hard to see unless you enlarge these images, but you should see one, two, four, eight, numerous lines on the time series plots (points on the orbit diagram) for r=2.95,3.01,3.52,3.555,3.57, respectively.

Logistic Map

This is an orbit diagram for the logistic map. It shows how the period doubles for various r values along with windows where the period reduces. Approaching these windows, the output is aperiodic (chaotic)...I think I can say that and it's true. The growth parameter (x-axis), r ranged from 2.9 to 4 and is incremented by 0.001. For each r value, there are ~200 output values (y-axis). I only took outputs after the system reached steady state (eyeballing - half of total iterations). The initial input to the map is 0.5 (so the initial output is based on this...output = r*input*(1-input) ). Since this is a nonlinear map, the input generates an output which then becomes the new input, and repeat for many iterations. For some reason after r = 4, the system blows up after a few iterations...I'm not sure what to say about that right now.

Edit: The system blows up for r > 4 because input/output is bounded by 0 and 1. The map is a parabola with it's maximum at output = r/4...this assuming 0<=input<=1.

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?

Failed mappings

The ones that look like a play button and a jelly fish should be sanddollars.  The sideways torch is supposed to be a diagonal line.  All are failed attempts at a program I'm working on, but they're still neat.

potential, potential difference, voltage, volts

Voltage means potential difference.  So when someone says, "The voltage of that power line over yonder is at 10kV."  What they mean is that the potential to which the wire itself is set is 10kV ABOVE the potential of the earth or ground.  Typically we take ground to be zero volts, but the 10kV has to be in reference to something standard.  Otherwise, it makes NO SENSE to say something is just at "blah" volts, unless it's in reference to something everyone listening understands what the implied reference is.  Therefore, people who don't REALLY know what they're talking about in say a scientific situation where everyone should be on the same knowledgable page should make sure to include to what their potential is referencing.

ALSO, volts is only the unit of potential and thus potential difference (voltage), SO you cannot interchange the words to hope for the same meaning in what you present.

flame

Instead of laying down to read as I had initially planned about twenty minutes ago, I've been downloading my photos.  While they transferred from camera to computer, I watched my candle light flickering.  No no, I'm not sitting in the dark with the glow of my computer screen and one lit biscotti scented candle as I may have made you imagine.  I've my corner medusa lights on too.  Back to my biscotti light.  

Nope.  

I just went on a net-tangent reading about the earth's magnetosphere...at least it's relevant.

Despite a simple candle flame not truly being a plasma, I still think it exhibits a very similar structure as the auroras.  If you look closely, the tip of the flame sometimes has noticeable cuts jutting into it to make it look like the curtain shape of the auroras.

Maybe that's god's way of giving a little bit of spectacular lights to anyone who can create a flame.

Awww.