Sierpinski Tetrahedra at Boyce Thompson Arboretum





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These first two rows of images have no Sierpinski tetrahedra in them. Instead, I have put up a few images of my granddaughter that show the arboretum from a bigger view. The left image was taken at Boyce Thompson's demonstration garden. The bridge in the above-middle picture is Outback Bridge that crosses Silver King Wash. The bridge in the second row is new, and it crosses over the Queen Creek river to the arboretum's High Trail. Photos from the 3rd row down show isolated blossoms and up-close views of the arboretum against the tetrahedrons.


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My granddaughter especially loves the bridges, and they are safe for children. There is a lot of open ground to run on, too. There are places where you have to stay on the trail, but even then, the trails are wide and well-maintained. In the photo on the left, she was mesmerized by a photographer taking pictures of birds. The Boyce Thompson Arboretum is home to lots of birds and early morning bird watchers.






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This second set of photographs was taken looking through Sierpinski tetrahedra in Spring 2004. The big thing to notice when looking at the structures: the parts are similar to the whole structure, and you see the same shapes on different scales. These properties are fundamental to fractals, and are shared by many aspects of nature such as the limbs in trees and bushes: little limbs closely resemble big limbs in a given tree or bush.


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Much of the plant life on this page, as well as other photographs I've taken at Boyce Thompson, have been identified by horticultural specialist Kim Stone. The information either came from Kim, or from a sign posted at the location of the plant. In the enlargement of the periwinkle colored flower above-left, there is a small bug taking refuge in the center of the flower. There is also a tiny, redish-colored spider or mite on the yellow flower second row up, far-right image.





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Two of my original Spring 2001 images. In the left image, a stage-4 Sierpinski Tetrahedron is sitting next to a river called Queen Creek that runs through the arboretum. The Town of Queen Creek was named after the river. There are some nice shadows on the rock made by the tetrahedron. Changing gears, can you see the hidden stage-2 sitting in the beautiful Japanese Quince in the image on the right? The tetrahedron is painted in quinacridone red.





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The images in the rows directly above and below are from a set of images taken along Queen Creek in late November 2003, in a deeper section of the arboretum. The tetrahedron is reflected in the water in the far-left image. The other two images are from the Creek, but no tetrahedra are shown in the images. I particularly like the image on the far-right. The log is shown in perspective with its surroundings in the middle picture.


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On the left, pink Sierpinski Tetrahedra are sitting in a Blue Bush (Maireana sedifolia) from the Goosefoot Family, native to Australia. I recall tiny blooms covering it that were almost the same color as the tetrahedron. The right image is of a stage-3 sitting in a grass called Regal Mist (Muhlenbergia capillaris), native to Mexico.





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As of the time of putting up the above two pictures, I don't have names for the plants in them, as they are in an area of the arboretum that is dense with plants. The yellow structure in the picture on the right is the Complement for the stage-4 Sierpinski Tetrahedron (it represents the volume that has been removed from the stage-4).





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On the left is a stage-4 Sierpinski Tetrahedron with a River Bushwillow Tree. In the middle, an inflatable tetrahedron and octahedron are sitting in a Streaked Wattle (Acacia, lineata) from the Pea family in Australia. In the last picture, the same inflatables are on the rail of the Outback Bridge. I took the inflatables out because it was raining, as discussed in next row of images.





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On the left is a stage-3 Sierpinski painted in iridescent russet sitting in a Lerp Mallee (Eucalyptus incrassata), from the Myrtle Family in Australia, taken in 2002. In the middle and right images are two of the platonic solids, the tetrahedron and octahedron, taken December 2004 in the rain, sitting in the same tree. It was raining so I brought out my inflatables, and only had two on hand,





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The middle picture shows a stage-3 Sierpinski Tetrahedron painted in iridescent russet sitting in a Fluted Horn Mallee (Eucalyptus stowardii) from the Myrtle Family in W. Australia.






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Stark yet beautiful, the shadows on the rock wall in the left image are adorned by a leafed branch growing right out of the rock. The middle image is cropped way down, the hummingbird was in a small section of the original. I just like the colors in the image on the right, the gold tones are very pretty.






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Taken along Queen Creek in November 2003. I didn't have the tetrahedrons with me the day these were taken. The image on the right was taken in the cultivated section of the arboretum.





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