Beauty in the eyes of the beholder; blizzards, construction sites and mathematic equations!

Having just been inundated with 20+ inches of snow in a furious 24 hour blizzard (that most of the nation experienced in some way), I am surrounded by the inconvenient beauty of snow and ice covered windows, huge, swirling drifts and unplowed roads. I realize that some do not enjoy winter or snow, but who could argue with the utter beauty left behind a snowfall? Not certain of the actual snowfall in our area, there are 4-5 foot drifts virtually everywhere. Just as my husband cleared a path of the huge drifts that consumed our drive way, the snow started again and left what looked like another 7 inches! The town we live in was at a standstill, roads remained mainly un-drivable 12 hours later, but thankfully we experienced no power outages or major problems. We just stayed inside for a snow day. I took the photo below of our patio from out the back window. Since first posting this, I went outside in the sun today and took a few more photos but the pristine snow drifts were mostly replaced by shoveled and plowed banks. Our neighbor's yard is still mostly untouched, as the snow is past their children's heads!

My  son often sends me odd but interesting creative links, for which I am grateful. I have used a few of them in this blog and I hope you enjoy the variety. Several months ago he sent a YouTube clip of a guy supposedly creating a picture of the Mona Lisa with a nail gun, from about 10 feet away. Although it was a clever production, the construction experts in our home agree that it wasn't real! This Nail Art, below, IS actually created by hand, however,  with roofing nails (on a 4' x 8' sheet of plywood!). While I wish the artist had used his skill to create an original image, rather than using a Leonardo Da Vinci drawing (just the teacher in me), this amazing, innovative 3-dimensional art creates shading with nails set at various heights. Cool medium and technique. I don't know anything about the man who created this work of art, and I'd really like to see more of his work. (I wonder where the idea originated? Did he spend time as a roofer?) Below are just a few of the images, click here for more pictures.

NOW, on a completely different, very left-brained note, the video clip below was sent to me by Edwin L. Kerr, Ph. D. in Theoretical Physics; I just met Edwin last week. He had visited  my blog through a link from another site and our conversation was about the beauty of creation, even in unsuspected areas, such as mathematic equations; specifically, the beauty of fractals. (Yes, I said fractals.) Among many other things, he has worked on projects for NASA and is confronted with the beauty hidden in math and science on a regular basis. He noted that while calculating mathematic equations may not lend itself to public exhibition and appreciation, he was able to utilize both right and left brains to create this 1 minute 45 second graphic interpretation of what is known as the Mandelbrot Set, which he finds creative in nature and its beauty causes him to worship the Creator of it all. It is a mathematical equation I cannot hope to explain, so I will let Edwin explain in his own words, below. The point is, however, that you don't have to understand the mathematics to appreciate its beauty (although it does have a bit of psychedelic feel, doesn't it!). I am always astounded to see creativity expressed in new places (new to me anyway!). Thanks for sharing!

Edwin Kerr's explanation:

Benoit Mandelbrot found a way of expressing graphically the beauty hidden in a simple mathematical equation.  The equation defines what is now known as the Mandelbrot set.

The set is a black cardioid shaped object at the center of the screen.  It has various bulbs (roughly circular black spots) attached.  From these bulbs emanate a set of black filaments, usually too fine to see.  Along the branches there sometimes appear small satellite Mandelbrot sets.  The filaments have many branches.  I have discovered a way of localizing the tips of the branches.

One could think of the Mandelbrot set as a very spiky iron object that needs paint.  The first coat of paint becomes very thin at the tips of the points but it collects and thickens where the branches join each other or join the bulbs.  This makes the painted object smoother than the original.  Successive coats of paint are smoother still because the underlying coats have rounded the points and filled in the joints.  The outermost coat is a circle that encloses everything.

In the movie the view zooms in on one of the points.  At first the point seems like a little protrusion on one of the bulbs, but on closer examination one sees that the inner filament is a stem that branches into a star with six arms, arms of various lengths.  As the movie continues to zoom in on the tip of the shortest arm one sees that the arm ends in another, smaller star, also with six arms, and that the arm we are focusing on is really the shortest arm of the smaller star.  The process of zooming in continues, revealing more and more stars in the arms of stars, with no known limit.  One can see that the arms curve around because the general picture revolves around the center as the movie zooms in.  The movie only shows the first 180 of the outer coats of paint.  Eventually when it runs out of colors it shows the outside of the next layer as a black skeleton embedded in the stars.  The skeleton shows where the filament lies, still supposedly coated with an infinite number of other layers of paint that can’t be pictured without letting the computer run too long.

It took about four days of running time to make this movie.  That time is short compared to the five months I have heard quoted for comparable movies.  Mandelbrot computed the Mandelbrot set by taking differences of numbers that are nearly equal.  Zooming in to greater magnifications has until now meant computing the numbers with greater and greater precision, and that has meant letting the computer run for a long time.  I discovered a way of working with the differences directly and don’t need high precision.  My method stays centered on the tip even when the magnification becomes much greater than the precision with which the tip’s location is specified.

I have discovered about 1500 of these points but naturally have not been able to explore them all.  I have made only four or five movies of this type so far.

People say that beauty is in the eye of the beholder.  However, the creation story shows that beauty exists objectively, independently of what people think.  The Bible says “And out of the ground made the LORD God to grow every tree that is pleasant to the sight, and good for food; the tree of life also in the midst of the garden, and the tree of knowledge of good and evil.(Gen 2:9)”  The trees were both useful and beautiful.  Their beauty is objective because God made them that way.