Day 4: Leona Gorge

I’ve been a bit behind on my posts because I’ve been having to fix the technical difficulties on the students’ blogs.  Therefore, I am going to skip my photographs from the Fort Funston trip (for now) and go straight to our Leona Gorge trip.

A Taste of the Bubbley

A Taste of the Bubbley: The shade in the gorge allowed me to use a slow shutter speed, which led to the great time-lapse effect in this photo.  The strange patterns in the water are how the motion of a tiny waterfall were captured by my camera.  The big bubble is actually a conglomeration of many bubbles that were forming and popping while the shutter was open.

Lizard King

Lizard King: This little guy allowed me to go right up to him and capture a nice shot.  His pose across the edge of a rock gives a nice contrast between the light rock face and its dark side.  The lizard itself has lots of great repeating patterns across its back.  Click on it for a closer look.

Jagged Little Leaf

Jagged Little Leaf: This is a really interesting plant whose leaves unfold into a fern-like shape with jagged edges.  I like how the photo shows many different stages of thus unfolding.  I also love the complex layout of many copies of a simple pattern.

Snail Jail

Snail Jail: Okay, so it doesn’t really look like a prison, but I wanted to keep the rhyming theme going.  I love the lighting here and how the fractal pattern of the trees bark contrasts with the pattern on the snail’s shell.  I found this little guy in the Horticulture Building at Merritt College at the end of our hike.

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Day 1: Lake Merritt

When we began this field trip, I was worried that I would be taking pictures of the same things as last year.  However, I was surprised and delighted to find many new patterns that I hadn’t discovered before!

Burton's Bride

Burton’s Bride: At first I was going to delete this photo of a bird (I’m not sure what type, but I’m sure Mr. Miller will fill me in) in Lake Merritt.  However, Ashley pointed out what a great optical illusion that this image is!  After she noted that it looks like a Tim Burton-esque bride with long white hair, I couldn’t see the bird in the picture anymore.  How about you?

Fractal Stalk

Fractal Stalk: This stalk shooting out from the top of a succulent in the Botanical Gardens is an excellent representation of a self-similar fractal.  Each of the branches appears to be the same as the whole thing!  I think that the angle I took the photo at really shows off this structure.

Simplicity

Simplicity: I picked this photo to share because I think it shows that a very simple pattern can also be very beautiful.  Each of the stems are almost identical and ALMOST symmetrical.  Notice, however, that the leaves are slightly offset form each other on either side of the stem.  The blue background and splash of sunlight really bring out the beauty in this pattern.

Fractal Fronds

Infinite Fronds: I took this photo by standing under a “Blue Palm” and taking a picture of the fronds backlit by the sun.  Palm fronds have a really great radial pattern, and the arrangement of the fronds and their shadows in this image make me imagine fronds going into infinity (and perhaps beyond).

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2010

It’s a new year and a new post-session!  I’m looking forward to revisiting many of the places I photographed last year to find new patterns and new perspectives with a new group of students!  Stay tuned…

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Final Reflection

It’s hard for me to say whether or not this class is what I expected because I didn’t know exactly what to expect.  You never know what a class will turn out like because it depends so much on the attitudes of the students. Mr. Miller and I  developed a strong idea for what we wanted the class to be like:  lots of exploration and questioning.  Mostly, this was very successful.  Many students took to the freedom and used the time and opportunities we gave them to take their learning to a new level.  A few wasted their time and didn’t take things seriously.  To really judge things, though, I am going to have to focus on the first group because they are the ones we did this for.  I think that they discovered things about themselves and how they learn that will aid them in their futures.  I am so proud of what they accomplished!

I am going to take SO MUCH away from this class.  First of all, the hikes that Mr. Miller showed us were unbelievable and I can’t wait to visit some of these spots again.  Of course, it won’t be the same without the whole crew!  I am also taking away a deeper undersanding of Geometer’s Sketchpad and Cellular Automata.  These are two things that I’d never really been able to play around with and explore until now.  I’ve also made my first blog, which was a great experience!  The biggest things I will take have to do with the students.  First, I will take away some of the relationships I’ve built with the young adults in the class.  Some students I already knew well (such as my advisees), and our bonds were strengthened.  Others I was able to work with for the first time (Marquinika, Brenda, Karla, Dennis, Jessica, Lucretia).  These relationships and what I’ve learned from each student have changed my iterative path ever so slightly–but who knows what the Butterfly Effect has in store.  Another thing about students that I will take away is how they have an innate curiosity that is sometimes buried by the piles of “muck” they must learn in their regular classes.   These are important no doubt, but if a student has never been given the freedom to explore on their own, it is much less meaningful.  I was amazed at how giving the students cameras and a simple assignment to “find patterns” shifted their focus from socializing to searching for what makes the world around them move as it does.

The hardest thing was organizing the countless ideas and experiences that I wanted to share with my students.  There is so much I know they would benefit from seeing, but we had to try and draw a fine line between doing the right amount and DTM.  In the end, the organic nature of our planning put us right at that magical edge between order and chaos.  Another hard thing was for me to stop teaching and learn.  There is so much I can teach my students, but there is just as much that they can teach me.  I feel that I did accomplish this, however, and was able to help my students develop their own ideas and learn from what they had to share.

During this post-session, I learned how to use my camera to take much better close-up macro shots.  I usually take mostly landscape shots when I’m exploring nature because of the difficultites I’ve had with focusing on small objects.  Nevertheless, I was able to take some incredible close-up shots during our journeys and I now have an additional item in my photographer’s bag of tricks.

To close out my reflection I want to thank every single one of my students.  You all inspire me to keep working hard for you even though I won’t be teaching next year.  I hope you will keep working hard for yourselves!  I also want to thank Mr. Miller for mentoring and teaching me these last couple of years.  Aside from the new things you have shown me, you have also been a great sounding board for me to develop my own ideas and theories.  I hope we get a chance to run this postsession again!

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Sierpinski Triangle

I created this Sierpinski triangle in Geometer's Sketchpad by iterating the following algorithm hundreds of times:  Find the midpoint of each side of the triangle.  Connect the midpoints to form a new triangle.  Remove the inner triangle.  I ended up with this self-similar design.  This means that if you zoom in on any of the smaller triangles, it will look exactly like the entire figure!

Sierpinski 1: I created this Sierpinski triangle in Geometer’s Sketchpad by iterating the following algorithm hundreds of times:

  1. Find the midpoint of each side of the triangle.
  2. Connect the midpoints to form a new triangle.
  3. Remove the inner triangle.

I ended up with this self-similar design. This means that if you zoom in on any of the smaller triangles, it will look exactly like the entire figure!

Relaxed Sierpinski:  Some students found that if you relaxed rule #1 so that the inner triangles did not have to be on midpoints, you got some interesting new fractals.  Here is mine.  It's interesting how simply removing regularity makes the fracal somewhat sinister.  Notice that it is still self-similar however!

Relaxed Sierpinski: Some students found that if you relaxed rule #1 so that the inner triangles did not have to be on midpoints, you got some interesting new fractals. Here is mine. It’s interesting how simply removing regularity makes the fracal somewhat sinister. Notice that it is still self-similar however!

Cellular Sierpenski:  This is the same design as the shape above made in a completely different way.  I made this using a 1D cellular automata program with rule 90.  The program builds each successive line using a very simple set of rules on the line above. This is after about 100 iterations.

Cellular Sierpenski: This is the same design as the shape above made in a completely different way. I made this using a 1D cellular automata program with rule 90. The program builds each successive line using a very simple set of rules on the line above. This is after about 100 iterations.

Cellular Sierpenski 2:  This is the same rule after about 40,000 iterations.  Even though I've zoomed out, the shape still looks the same.  It now has over 17,000,000 squares!

Cellular Sierpenski 2: This is the same rule after about 40,000 iterations. Even though I’ve zoomed out, the shape still looks the same. It now has over 17,000,000 squares!

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Exploratorium

Fractal Cube:  This cube hanging above the entrance to the Exploratorium is not quite a three dimensions, but it is certainly larger than 2.

Fractal Cube: This cube hanging above the entrance to the Exploratorium is not quite a three dimensions, but it is certainly larger than 2.

Ice Crystals:  These fractal crystals form when water freezes.  You can actually watch as the branching pattern iterates accross the surface of the glass to form these shapes.

Ice Crystals: These fractal crystals form when water freezes. You can actually watch as the branching pattern iterates accross the surface of the glass to form these shapes.

Chaotic Diffusion:  Just like in the cellular automata, the simple rules of thermodynamics lead to the chaotic mixing of the two fluids.

Chaotic Diffusion: Just like in the cellular automata, the simple rules of thermodynamics lead to the chaotic mixing of the two fluids.

Chaotic Diffusion, Part Deux:  Again the laws of thermodynamics lead to chaos.  This time, the fluids are the same--air--but the fluid heated by the filament has different properties which appear in the shadows as it mixes with the cooler air.

Chaotic Diffusion, Part Deux: Again the laws of thermodynamics lead to chaos. This time, the fluids are the same–air–but the fluid heated by the filament has different properties which appear in the shadows as it mixes with the cooler air.

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Cellular Automata: The Game of Life

The Game of Life is a 2D cellular automata where cells either “live” (turn black) or “die” (turn white) based on how many other cells around them are alive or dead.  When you iterate, the cells interact to produce potentially complex patterns.  Below is an interesting pattern that I found that is not chaotic but reproduces the initial set up..

Generation1:  Starting with this pattern, it remains stable for infinite generations unless something is changed from the outside.  When a living cell is added to any corner, the shape begins growing.

Initial Condition: Starting with this pattern, it remains stable for infinite generations unless something is changed from the outside. When a living cell is added to any corner, the shape begins growing.

Generation 5:  After 5 generations, a very similar but much larger shape appears.

Generation 5: After 5 iterations, a very similar but much larger shape appears.

Generation 14: The initial shape has now blown up into this symmetrical "snow flake".

Generation 14: The initial shape has now blown up into this symmetrical “snow flake”

Generation 17:  After 17 iterations, the intial shape has been reproduced into 4 exact versions of itself.  If we were to add another living cell to a corner, the 4 would interact in a seemingly chaotic manner.  However, this current pattern would stay stable for inifinite iterations.

Generation 17: After 17 iterations, the initial shape has been reproduced into 4 exact versions of itself. If we were to add another living cell to a corner, the 4 would interact in a seemingly chaotic manner. However, this current pattern would stay stable for infinite iterations.

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