On Exploring a Natural Pattern

Everything must be made as simple as possible. But not simpler. (Albert Einstein, physicist)

Paul Green, at Stanford, has argued persuasively that the Fibonacci series is just what one would expect as the simplest self-repeating pattern that can be generated by the particular growth processes in the growing tips of the tissues that form sunflowers, pine cones, and so forth. (Stuart A. Kauffman, MD)

The most beautiful thing we can experience is the mysterious. It is the source of all true art and science. (Albert Einstein, physicist)

Without mathematics there is no art. (Luca Pacioli, mathematician and collaborator with Leonardo da Vinci)

56 thoughts on “On Exploring a Natural Pattern

  1. The quotes and video are simply beautiful, so simple and eloquent. We have both applauded the Fibonacci series before–it is still so very amazing! Art, music and math–what a great trio!


  2. Albert Einstein was referring to the golf swing when he said: “Everything must be made as simple as possible. But not simpler.”


  3. Love the Fibonacci Sequence.. And always marvel at the Mathematics within Nature.. Creativity showing us how we are all of us within this frequency.. The Sunflower has long long been my own symbol of Life’s seeds.. and the imagery here shows again how perfect Life is.. 🙂
    Wonderful share Frank..

    Enjoy your weekend.. Sue ❤


    • I agree with you, Carrie. Kauffman says that what we see is what should be expected, given the molecular processes involved in plant growth and other natural forms, whereas Albert terms it “mysterious”. Also, I think Pacioli phrases it wrongly when he says:

      Without mathematics there is no art..=

      Even without math, the golden ratio, or an approximation of it, would seem more pleasing to the eye than other ratios. Now, is that mysterious? Maybe. Perhaps it’s pleasing because symmetry with nature in general conveys a sense of order and control? Any psychologists want to weigh in on this?

      Liked by 1 person

      • Jim,
        We know the golden ratio is mathematical, especially as compared to other ratios. But art, maybe by its very nature, is very mathematical. So I wonder, if this isn’t a “chicken or the egg” discussion. Oh no … we’re getting too philosophical. 😉


  4. For many years I worked on the faculty of an art college and lived with a teacher of mathematics. Fibonacci, the golden section, lines, curves, proportions etc…were constantly our concern, as were the usual questions about beauty, inspiration, creativity…… Leonardo da Vinci was an example of the consummate artist/mathematician…..I think the moments when we are measuring the world and the moments when we are just marveling at its beauty, though those moments may not always coincide, they are all part of the great ever-evolving mental picture.


    • Cynthia,
      Thanks for the well-done analysis … and not too philosophical. 😉 … Another art teacher once told me that nature has the best designs, and artists are simply trying to duplicate them in their own way.


  5. Beautiful video!
    Interesting quote by Pacioli. As an artist, I don’t think I’m thinking mathematically at all when I’m creating. Now that I ponder that thought, I realize math comes into the equation somewhere even if it’s as cheeky as how much fabric & paint can I afford on my budget. LOL


  6. Wow. Loved this, Frank. It’s an amazing thing, isn’t it? I think I mentioned my interest in this as well as the golden ratio a while ago to you. I’ve had many philosophical discussions on this stuff that can really make your head hurt after a while! Thanks for this beautiful post. 🙂


  7. For someone who has never been much of a math-head, Frank, this was very easy viewing. Are you aware that the neurologist and author, Oliver Sacks, is dying? In theory, the second we’re born we start dying, but he is now terminally ill with cancer. He wrote a lovely Op-Ed piece that appeared in the New York Times. I think you’d like it: http://nyti.ms/1VETZWl


    • Lame,
      The video is a good one, so glad it was able to reach you in an understandable way. … and thanks for the Sacks article. Very interesting … and love the way he used crystals from the Periodic Table.


  8. Some of my favorite things…Nautilus shells, sunflowers, dragon flies–what a fantastic way to admire and think about them. The quotes are really wonderful, too, Frank. I often notice order and synchronicity in nature and art, but I frequently forget that math is involved. The video is a fabulous reminder!


    • Debra,
      The link between math and art is stronger than we realize … probably because it’s so subtle … besides, most of us don’t think beyond the results on the canvas. Glad you enjoyed this.


  9. Math remains a mystery to me, despite I use it daily. Isn’t that the strangest thing? I loved this, every single time I see something like this I am enthralled, I watch more than once just to absorb.


    • Val,
      As you mentioned, math is very much part of our daily lives … and probably even more than we suspect. Nonetheless, the quality of the video and the choice of music does a great job of drawing us into the theme.


  10. This is one of my very favorite videos ever, Frank! I’ve watched it many times over the years when I want to be reminded of the beauty and perfection within nature. Thanks for sharing.


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