“…art cries out for an artist. It is plainly impossible that so standard a work as the Universe should remain anonymous.” – G.K. Chesterton
One morning my sister-in-law captured a photo of the top image that was left on her windshield following a below freezing night. Before scraping the windshield clear, the photo was taken from inside the vehicle and preserved. Jack Frost, depicted on the left, in using my sister-in-law’s windshield as his canvass, had left this awe-inspiring wintry portrait for us all to enjoy and marvel. Until the window pane came into practical use, Jack Frost had no medium on which to share his divine gift.
Starting in late 19th century literature, more developed characterizations of Jack Frost depict him as a sprite-like character, sometimes appearing as a sinister mischief-maker or as a hero. He is traditionally said to leave the frosty, fern-like patterns on windows on cold winter mornings and nipping the extremities in cold weather. Over time, however, frost has become far less prevalent in the modern world due to the advance of double-glazing, but Jack Frost remains a well-known figure in popular culture. He is sometimes described or depicted with paint brush and bucket coloring the autumnal foliage red, yellow, brown, and orange.
As a retired high school mathematics teacher of Algebra and Geometry, the frozen design caught my eye and brought to mind a special branch of mathematics; fractal geometry.
Benoit B. Mandelbrot (20 November 1924 – 14 October 2010) was a Polish-born, French and American mathematician with broad interests in the practical sciences, especially regarding what he labeled as “the art of roughness” of physical phenomena and “the uncontrolled element in life.” He referred to himself as a “fractalist”. He is recognized for his contribution to the field of fractal geometry, which included coining the word “fractal”(see the image to the right of Jack Frost), as well as developing a theory of “roughness and self-similarity” in nature. Mandelbrot was one of the first to use computer graphics to create and display fractal geometric images(see the complex colorful image furthest to the right of Jack Frost), leading to his discovering the Mandelbrot Set in 1979. He showed how visual complexity can be created from simple rules. He said that things typically considered to be “rough”, a “mess” or “chaotic”, like clouds, shorelines or mountains, actually had a “degree of order.” Our frost-fern, since a part of nature, in like manner, does not satisfy the rules of classical geometry.
The frost-fern would be found by most to be a thing of beauty. An inquisitive child without cynicism would believe that it was fashioned by an impish fellow named Jack Frost. Mandelbrot, through fractal-geometry, brings order to the chaos of the image. In so doing provides an explanation and purpose behind its beauty.
While everyone is delighted by beauty, and the more alive among us are positively fascinated by it, few are explicitly aware that we can recognize truth by its beauty and simplicity. Most eminent physicists of the twentieth century agree that beauty is the primary standard for scientific truth. Likewise, the best of contemporary theologians is also exploring with renewed vigor the aesthetic dimensions of divine revelation. Honest searchers after truth can hardly fail to be impressed that these two disciplines, science and theology, so different in methods, approaches and aims, are yet meeting in this and other surprising and gratifying ways. – Thomas Dubay (The Evidential Power of Truth and Beauty)
The fern-frost design on the windshield is evidence of both truth and beauty. Truth in the sense that it IS, and that some action formed it. And beauty in that it impels appreciation from the witness. Jack frost, in the imaginative and wondering mind of the child, is seen as a marvelous impish instrument of the Divine Artist in His own creation. A finished novel proves an author. An existing building proves an architect. A rescued damsel proves a hero. The forgiven sinner proves a savior. And our frozen art proves an artist.
A child, again in the frost-fern, sees the artist as magical. But, by the premise that beauty is truth we can see the artist as mystical. As the pencil is the medium by which we lay down our thoughts; so, too, our universal natural environment is the medium by which God conveys His one all-inclusive thought. Whether this chaotic yet ordered incident of nature is believed to be the work of fairyland, or of scientific cause, the certainty is this; that it catches the imagination, compels inquiry, inspires human wonder and inclines the practical thinker toward the impractical.
The frost-fern is not an accident of nature. But, rather, is the intent of a loving God, whose purpose is to instill in the hearts of those who are captivated by such natural events that they need not fear any feeling of being lost, alone or abandoned. For what they see before them is in reality a divine gesture communicating the most desired comforting reassurance; “I AM here!”
The mercy of God has provided the tools of science and study of theology to once again allow fallen man to re-discover his Creator through understanding that which His creation reveals.
For those who are interested in viewing some awesome fractal designs , go to You Tube and key in: “Fractals The Hidden Dimension.” You won’t be disappointed.
Love this post Alan – thank you! ❤
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Thank you, Diana! Your opinion always valued and appreciated.
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