Self-Similarity

Saturday 7/13/2013 6:15 AM

My psalm for the week is Psalm 104.  In it the writer describes God and his creation.  It seems that everything has its place.  Water goes to valleys, flowing through the mountains on its way and quenching the thirst of living things.  Birds live in the skies and nest in trees; grass and plants are food for men and animals; storks live in junipers, goats in high mountains, and the hyrax in the crags.  Some animals prowl in the darkness, others are active during the day, some live on land, others in water.  God sustains everything.

The other day I was sitting on my back patio and I noticed a dead bug.  There were two different sized ants that were taking pieces of the bug away, I assumed to their respective nests.  As I looked I saw an extremely small bug, like a mite, that was also feeding on the bug’s corpse.  I thought immediately of the nursery rhyme Fleas, also known as The Siphonaptera.

Big fleas have little fleas,

Upon their backs to bite ’em,

And little fleas have lesser fleas,

and so, ad infinitum.

And the great fleas, themselves, in turn

Have greater fleas to go on;

While these again have greater still,

And greater still, and so on.

Lewis F. Richardson adapted the poem to describe fractal wind patterns:

Big whorls have little whorls

That feed on their velocity;

And little whorls have lesser whorls

And so on to viscosity.

I have often noticed that nature contains an incredibly large number of examples of self-similarity.  Broccoli and cauliflower florets break off into smaller versions of themselves.  The angle at which the branches grow from the trunk of a tree are the same for the same species of tree so that if the branches were cut off and placed in the ground they would look like smaller versions of the tree.  Both large and small mountains in a mountain range will often have the same shape.  Clouds in the sky are similar for each cloud group.  Galaxies and snails have different sizes but the same shape.  It is almost like things come in families, similar to the members in the family but different from other families.

The variety of both living and non-living things is nearly uncountable but God made it so that each thing would have its own niche in which to live and thrive.  His handiwork is on display regardless of the scale from which we observe it.  How cool is that?