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.