Day 7: Chapel of the Chimes & Mountain View Cemetary

This is one of my favorite places in Oakland and I go there to take pictures often.  Here are some of the shots I took looking through the lens of “Patterns in Nature”.

The leaky faucet in this pool makes perfectly concentric circles in the water.

Ring Pool: The leaky faucet in this pool makes perfectly concentric circles in the water on top of a chaotic tessellation.

This plant caught my eye as a perfect example of iterative, self-similar design.  The wirey stem makes the better very clear.

Wired Foliage: This plant caught my eye as a perfect example of iterative, self-similar design. The wiry stem makes the pattern very clear.

The lighting in the Chapel of the Chimes is beautiful and sets the scene for this lone flower.

Flower in Mourning: The lighting in the Chapel of the Chimes is beautiful and sets the scene for this lone flower.

I LOVE this shot and I think it is one of my favorites so far.  The bend in the leaf around the major veins creates intersting color and focal changes.  Within the center section, the veins also create a pattern very reminiscent to Hilbert's Space-Filling Curve (below).  Nature uses these types of fractal shapes to fill space as efficiently as possible.

Space-Filling Leaf: I LOVE this shot and I think it is one of my favorites so far. The bend in the leaf around the major veins creates intersting color and focal changes. Within the center section, the veins also create a pattern very reminiscent to Hilbert’s Space-Filling Curve (above in red). Nature uses these types of fractal shapes to fill space as efficiently as possible.

Tree

Tree: Sometimes it is nice to remind ourselves that the most visible and perhaps definitive example of a natural fractal is a tree.  Looking up into this one, I can see the overlapping layers that form a beautiful and regular, yet fractal pattern.

5 is the magic number for this plant.  How many places can you find 5?

Five Fingers: 5 is the magic number for this plant. How many places can you find 5?  This reminded me of the hand fractal below it.

Summit:  These are the brave souls that made it to the summit of Mountain View Cemetary.  They were rewarded with this incredible panoramic view of the Bay Area.

Summit: These are the brave souls that made it to the summit of Mountain View Cemetary. They were rewarded with this incredible panoramic view of the Bay Area.

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Day 6: Leona Gorge

This was a very challenging uphill hike with lots of amazing fractals and a great view of the city.  Enjoy!

This one is pretty self-explanatory, but I like how the branching continues even under the waterline.

Branching Roots: This one is pretty self-explanatory, but I like how the branching continues even under the waterline.

I mostly like the colors in this one.  The bright green and blue contrast nicely and the puffy clouds mimmic the gaps between the leaves.

Sky Blue Sky: I mostly like the colors in this one. The bright green and blue contrast nicely and the puffy clouds mimmic the flowers that are mixed in with the leaves.

There are 3 different patterns in the water in this photo.  The chaotic waves become very regular as the water goes through the chute.  Once it drops into the lower pool, the water becomes even more chaotic than before.

Waves of 3, Wave to Me: There are 3 different patterns in the water in this photo. The chaotic waves become very regular as the water goes through the chute. Once it drops into the lower pool, the water becomes even more chaotic than before.

I wish the focus was a little better, but I like how the web connects to the spikey spheres.

Webbed Spheres: I wish the focus was a little better, but I like how the web connects to the spikey spheres.

I think Fractal Fennel could replace the Oak Tree as the symbol of our city.  Then, they could pay me a bunch of money to use this as their publicity photo!

Fennelland: I think Fractal Fennel could replace the Oak Tree as the symbol of our city. Then, they could pay me a bunch of money to use this as their publicity photo!

Cool focus.  Can you see the hidden fennel?
Cool focus. Can you see the hidden fennel?
A forest at the base of a tree.  Self-similarity, ho ho, he he.

Forest of Moss: A forest at the base of a tree.  Self-similarity, ho ho, he he.

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Mandelbrot Set

The Mandelbrot set is the most famous fractal in the world.  It’s created with a very simple equation: z = z^2 + c.  From simplicity comes infinite complexity.  No matter how much you explore and zoom, you will never find perfect repetition or regularity.  Here are a couple of interesting images I captured from the Mandelbrot Set.

This image looks like it's the full Mandelbrot set because it has the very iconic image in the center.  Nevertheless, this has actually been zoomed in about 10 times on the edge of the original set.  Talk about self-similarity!  Also notice the great-great-great-great-grandbaby Mandelbrot under the large great-great-great-grandbaby.

Mean Green: This image looks like it’s the full Mandelbrot set because it has the very iconic image in the center. Nevertheless, this has actually been zoomed in about 10 times on the edge of the original set. Talk about self-similarity! Also notice the great-great-great-great-grandbaby Mandelbrot under the much larger great-great-great-grandbaby.

Mandelbranches:  This is at the edge between two mini-Mandelbrots.  The branches coming off of the edge of each begin to overlap here.

Mandelbranhes: This is at the edge between two mini-Mandelbrots. The branches coming off of the edge of each begin to overlap here.

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Day 5: Alameda Beach

I took this picture to show how the waves in the bay have left their imprint on the sand.  I asked Ashley to tell me where the water waves end and the sand waves begin and she pointed out that the water waves appear convex and the sand concave.  Very cool.

“And so waves made of sand melt into the sea…eventually”: I took this picture to show how the waves in the bay have left their imprint on the sand. I asked Ashley to tell me where the water waves end and the sand waves begin and she pointed out that the water waves appear convex and the sand concave. Very cool.

I took this picture because I thought it was interesting how the clam shell helped form the fractal pattern in the sand.  Karla pointed out that it looks like a bird.  I agree :)

Sea Gull: I took this picture because I thought it was interesting how the clam shell helped form the fractal pattern in the sand. Karla pointed out that it looks like a bird. I agree.

These tiny dunes form larger dunes that you can see if you look at the overlapping curves.  Or do the large curves form the small dunes?

Self-Similar Dunes: These tiny dunes form larger dunes that you can see if you look at the overlapping curves. Or do the large curves form the small dunes?

Besides the incredible confluence of color, I am drawn to this picture for how the forces of the patterns of wind and tide have shaped these three media in completely different ways.

Water, Sea Weed, and Sand: Besides the incredible confluence of color, I am drawn to this picture for how the forces of the patterns of wind and tide have shaped these three media in completely different ways.

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Day 4: Ocean Beach / Fort Funston

I never realized that this branching tree pattern was on the bottom of sand dollars.  As you can see in the next few photos, this pattern is repeated a lot in nature!

Dollar Tree: I never realized that this branching tree pattern was on the bottom of sand dollars. As you can see in the next few photos, this pattern is repeated a lot in nature!

This seaweed has the same branching pattern as the sand dollar.  Besides the pattern, I also like how I framed this shot.

Sea Tree: This seaweed has the same branching pattern as the sand dollar. Besides the pattern, I also like how I framed this shot.

The erosion pattern in the sand also branches like a tree.  What's interesting is that this pattern grows in reverse from a tree--starting with the branches and combining to create the trunk.

Sand Tree: The erosion pattern in the sand also branches like a tree. What’s interesting is that this pattern grows in reverse from a tree–starting with the branches and combining to create the trunk.

The breaks in the sea foam also branches!  You can see a lot of similarity in the polygons created by the breaks as well.

Foam Tree: The breaks in the sea foam also branches! You can see a lot of similarity in the polygons created by the breaks as well.

Okay, so there aren't really any tree patterns here, but there always has to be an oddball.  I really like how the tides have shaped these rocks into such an interesting way and created this very neat arch.  Is the arch 1 foot tall or 10?

Rock Tree: Okay, so there aren’t really any tree patterns here, but there always has to be an oddball. I really like how the tides have shaped these rocks into such an interesting way and created this very neat arch. Is the arch 1 foot tall or 10? Also, notice the spiral swirls in the foam.

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Day 3: Lake Merritt Botanical Garden

Mr. Miller once again showed us an amazing part of Oakland that was hidden right before our eyes.  I live a half mile away from the botanical gardens at Lake Merritt but was completely unaware of their existence.  The amount of natural beauty I saw there overwhelmed the students and me.  The group split up some as we went on our independent hunts for the rarest photos.  At one point I spent 30 minutes taking picture of the same tree, trying to get it just right.  Needless to say, I ended up with 40+ incredible photos (IMHO) and there is absolutely no way to narrow it down to four.  Therefore, I am extending the number to 10 for the class as long as each photograph is defended with a thoughtful and descriptive caption.

Test

Swaying Grass: The two things I love about this photo are the colors and focus.  I took this picture in the median at the intersection of Harrison and Berkeley on the way to the lake.   You’d probably never notice when you drive by in your car, but these plants show a lot of beauty when you take the time to look.

Fractal Branching

Fractal Branching: The self-similarity in this picture astounds me.  If you look in the spaces between branches, you see an iteration of branches growing with the same algorithm.  The angle of the photo and the deep focus highlight this feature.

Antennae

Antennae: I spent a lot of time looking a this tree.  It has very interesting self-similar patterns on its stems that are somewhat fern-like.  On this picture, however, I chose to focus on these two reproductive organisms at the base of the stem.  I love how the tiny spheres help build the larger one.

Ladybug Lane

Ladybug Lane: I spent a lot of time trying to coax this critter into a nice pose for my picture.  It is on the same tree as above, this time highlighting the leaves.

Veins

Veins: I’m not sure what type of plant this leaf was on, but the leaf itself was GIGANTIC.  I laid it over my lens and held it up to the light to get a series of shots of the veins.   They are all very cool, but Ashley thought this was the best.  They all show the bifurcating patterns that are similar to those of the branches and stems of the plant.  The bifurcations overlap to produce self-similar polygons at many different scales on the leaf.

Fractal Fern:  I couldn't pass up this perfect example of self-similarity.

Fractal Fern: I couldn’t pass up this perfect example of self-similarity.  I wish I had taken this with better focus so I could see more detail in the white patterns on individual leaves.

There was a large section of these flowers that radiated throw the green foliage.  This photo is the best from a series I took of the patch.  The flower in focus appears to float in a different universe from the flat background.  This effect is due to the differing heights of all the flowers in the bunch.

Flourescent Flowers (yay again for alliteration!): There was a large section of these flowers that radiated through the green foliage. This photo is the best from a series I took of the patch.  The flower in focus appears to float in a different universe from the flat background. This effect is due to the differing heights of all the flowers in the bunch.

Self-Similar Madness

Self-Similar Madness: Although I am not so pleased with the background and focus of this image, I thought it was an incredible example of a 3D self-similar fractal.  If I could zoom in even more, I wonder how many times this pattern would repeat.  Perhaps infinitely?

Purple:  I think this flower mainly speaks for itself.  It has perfect symmetry.

Purple: I think this flower mainly speaks for itself. It has perfect symmetry.

Untitled

Untitled: I don’t know how a title or caption could do justice to how this picture makes me feel.  The water droplets look like frost hanging onto the flower.  The bright green background is an excellent juxtaposition for the idea of frosty petals.  You can probably tell that the off-center flower and blurry background is becoming a motif for me.  I think I may have to continue it.

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