Fractals 

Portion of a Mandelbrot Set

A fractal is an entity that exhibits a repeating pattern.  Many patterns in nature exhibit fractal phenomenon and computer simulations are used to generate fractal patterns artificially.  Natural phenomena such as coastlines  exhibit a fractal pattern, as the pattern displayed may be exact (self-similar) or perhaps just similar at various levels of detail or magnification.  Snowflakes and trees property of continuing detail at higher levels of magnification.  Because of this, fractals are considered "nowhere differentiable" because of their inability to be measured traditionally.

Fractals are used in many fields, including physics, biology, medicine and physiology, imaging and financial fields. Fractals may apply in economic contexts such as the stock market Standard and Poors 500 Index, when examining longer term patterns (years) vs shorter terms (months, days, intra-day trading).  Fractals may be used in cinema, advertising, graphic design and climate science .  Fractals are a beautiful representation of art in their own way, in the visual arts, including the Droste effect, which is a picture within a picture. 

Fibonacci numbers, the basis of the Fibonacci Sequence appears in fractal geometry in a wide variety of ways.  Fractal dimension is a measure used to quantify complexity.  It measures  how detail changes with scale and the capacity of the fractal to fill space.  Various definitions of fractals and mathematical indicators exist, including a definition by mathematician Benoit Mandelbrot  who characterized a fractal as an object whose Hausdorff-Besicovitch dimension  is greater than its topological dimension. 

Wikipedia lists the Hausdorff-Besicovitch dimensions of a number of common fractals, including the Koch snowflake, Sierpinski Triangle, Quadric Cross, Julia Set and the Boundary of the Mandelbrot Set. Values for natural processes such as  the Coastline of Ireland , Great Britain and Norway are listed, as are values for various Brownian motion and random walk processes.  Dimensions are shown for biological models such as Cauliflower, Broccoli, the surface of the Human Brain , and the Human Lung.  Higher numbers indicate increasing complexity.

Fractals may be use in diagnostic medicine and physiology.  For example, blood vessels may exhibit fractal characteristics, as may the lung and surface of the human brain.  Tortuosity, another metric, relates the ratio of the actual length of a curve or segments of a curve to the distance between the two ends. Tortuosity may also reflect the degree to which a curve crosses over itself.  
  
Tortuosity was used for characterizing animal trails of mites  with regards to Brownian motion pathways.  Fractal dimension and tortuosity may both be used in measurement of blood vessels, as is shown in this article from the medical journal PubMed in a study of pulmonary hypertension.  In that study, distance metric, a measurement of tortuosity, was statistically more significant than the fractal dimension in correlating clinical patient parameters with the particular metric.   This goes to show that the use of different metrics may produce differing correlations, perhaps a clue in itself to underlying characteristic studied.

Fractals  form the basis of many aspects of life and the world around us, igniting our curiosity, aiding our research, informing us, and conveying a sense of beauty, form and function.

The Ginko Biloba Tree

Ginkgo Leaf Fossil, Burke Museum, University of Washington, Seattle, Washington

The above photo of the Ginkgo Leaf Fossil was taken at the Burke Museum, University of Washington, Seattle, Washington and  represents a fossil of a Ginkgo taken in Smithers, British Columbia, Canada.  Driftwood Canyon Provincial Park, in Smithers, is one of the world's most significant fossil beds.   

The Ginkgo Biloba tree appears naturally, in the wild, only in China.  It is grown in many place worldwide, as a cultivated tree, and adapts well in well watered and well drained habitats. Ginkgo Biloba is a living fossil , dating back 270 millions to the Permian Period  .  Ginkgo has managed to evolve along a very long evolutionary time period without much speciation.

It is an interesting example of a plant that has had extreme longevity, slow growth, late reproductive maturity and has survived through many diverse and disturbed environments, including the Ice Age .  It has  managed, despite  a narrow base of speciation to support it.  It has two sexes, male and female, and has its ability to exhibit clonal reproduction, a process which produces a population of identical units which reproduce from the same ancestral line. This has helped it survive evolutionary challenges.  The Ginkgo is also highly resistant to air pollution and grows in areas where air pollution has damaged other species.

A HHMI BioInteractive presentation discusses the issue of clonal reproduction in a video. "Are Males Really Necessary?"  using fruits and vegetables as props.   The video is thought provoking and uses creative use tools to discuss an educational subject.  The 23rd or "sex chromosome"  is a specialized area of interest not explicitly discussed.  Protocols for tossing out wilted lettuce or black bananas present an analytic challenge.

The black banana we consider tossing out might be more useful than the newest banana, especially if we are considering  baking banana bread to bring to the next potluck.  It takes awhile to produce the necessary senescence in a banana to get the right flavor and texture for banana bread.  Thus,  Interoperability, whether it be in bread making, computer engineering or other systems, is an important evolutionary issue, involving mutations along with a stochastic process.

One has to wonder at the combination of processes that has sustained the Ginkgo for million years as well as the diverse environments that the Ginkgo tree  has experienced.   Ginkgo is an herb.  Its leaves and sometimes its seeds are used to make extracts for medicinal purposes, including memory disorders such as Alzheimers and dementia.  Even as we consider the marvel that is the Ginkgo Biloba, we find fascination and beauty in its foliage, and comfort in the shade that it produces.  It is a tree and much more.

World Health Organization Report on Air Pollution and Health

                   Orca Whale, Haze, Strait of Juan de Fuca, British Columbia, 9/18/2012

A report released 3/25/2014 by the World Health Organization attributed one in eight deaths to the impacts from air pollution.   The report indicated that 7 million people died in 2012 as a result of air pollution, making air pollution the greatest single environmental health risk.   The WHO report provides fact sheets on Ambient (Outdoor) Pollution and on Indoor Pollution.   The WHO report displays a number of informative graphical presentations of the world wide distribution and impact of air pollution.  These presentations include the Exposure to Ambient Air Pollution and Mortality from Ambient Air Pollution.

 As the WHO graphs show, high income nations such as the United States had better air quality results.  The United States has a regulatory presence in the air pollution field with the Environmental Protection Agency, state agencies such as the State of Washington's Department of Ecology and local agencies such as the Puget Sound Clean Air Agency providing regulatory oversight. 

Air pollution is a global problem, as it can cross borders with global air flow.  The regulatory climate in one nation may impact other nations downwind from it. Thus nations are concerned about the regulatory climate in other countries.

The impact of air pollution goes beyond the health issues pointed out in the WHO article.  It also impacts economic relationships between countries.  Corporations arbitrage the cost in complying with air pollution regulations in their decisions as to where to locate by excluding the economic cost of externalities in pricing. 

Countries who do not have as stringent air pollution regulations will thus attract more business due to the lower costs associated with lesser compliance.  This results in consumers purchasing goods at lower prices, which do not reflect the externalities associated with the degradation in air quality. These externalities include the costs of increased morbidity and mortality of not only those in the area producing the pollution but in those areas downwind which may be subject to the pollution.  The downwind spread will reflect the nature of the pollutant and atmospheric conditions.

The above photo was taken in the Strait of Juan de Fuca between Washington State and British Columbia, looking west, through the haze, on a calm fall day.  The haze reflects the impact of suspended particulates, atmospheric aerosols, and the marine air mass.  Another photo, taken looking east on the same day, shows the impact of forest fires in Eastern Washington on air quality in views of Mt Baker and the Cascade Mountains.  

It is an interesting exercise to consider the relative contributions of air pollution from foreign and domestic sources.  This is especially challenging when atmospheric conditions encourage the mixing of different sources in a stagnant setting and contributions to health issues need to be considered.   An article in the Smithsonian (1/21/14) discusses contributions of air pollution from China to air pollution in the United States.

Flock of Snow Geese Taking off, Skagit Valley, Washington (blurredmotion)

Flock of Snow Geese Taking off, Skagit Valley, Washington (blurred motion), originally uploaded by Marilyn Dunstan Photography.

Snow Geese taking off in the Skagit Valley, Washington, shown in blurred motion.

These Snow Geese (Chen caerulescens), breed on Wrangel Island off the north coast of Siberia, and over-winter in the rich farmland of the Skagit Valley, in Northwest Washington. This flock is part of the Fraser-Skagit population, while the geese generally may visit the United States, Canada and Russia.

Pacific Science Center at Night (digital effect)

Pacific Science Center at Night (digital effect), originally uploaded by Marilyn Dunstan Photography.

The Pacific Science Center, Seattle, Washington was designed by Minoru Yamasaki and built in 1962 for the Seattle World's Fair. It hosts a planetarium, two IMAX theaters, a butterfly house and numerous science exhibits that make science come alive with interactive displays that give a hands-on-education to both young and old alike.

www.pacificsciencecenter.org

"Super Moon" Full Moon Rise over Seattle Waterfront, Seattle,Washington (defocused)

"Super Moon" Full Moon Rise over Seattle Waterfront, Seattle, Washington (defocused), originally uploaded by Marilyn Dunstan Photography.

Digital rendition of Super Moon Full Moon Rise over Seattle Waterfront, March 19, 2011

Fractal Julia Design

Fractal Julia Design, originally uploaded by Marilyn Dunstan Photography.

Fractal Julia Design - expressing the recursive aspects of nature via mathematical design.