Patterns

Patterns are everywhere in nature. From the cosmos down to it's constituent atoms we find recognisable patterns both in living and non living forms. On the larger scales are gigantic spirals of stars - the galaxies one of which we inhabit, planetary systems like our own solar system. In the living world are the beautiful shapes of flowers, patterns on butterfly wings, zebras  and in the microworld the geometrical forms of pollen, diatoms  and radiolarians to name just a few.

The laws of mathematics, physics and chemistry can be used to explain patterns in nature and these patterns can be modeled with computer simulations.

Below are some of the images I have taken over the years showing different patterns in nature. The list isn't complete by any means (I haven't managed to photograph snow crystals which show a six point symmetry  yet!).

See the article in Wikipedia 

M31 The Andromeda Galaxy is about 2,000,000 light years distant. I created this image by stacking dozens of images taken with a Canon 550d DLSR. The spiral structure and the central hub can clearly be seen. Research is still going on to determine how these spirals are formed.

A tree at sunrise taken a few miles from my home. Branching patterns here are of a fractal nature. The pattern being repeated at ever smaller scales.Mathematical algorithms can be used to simulate these tree patterns. Tree branching is typical of nature's use of self similarity with ever repeating patterns at smaller and smaller scales.

Another branching pattern formed by recrystallising a solution of baking powder (sodium bicarbonate). x40. Such branching crystals are called dendrites.

.Flowers often show rotational or radial symmetry as in this example from my local park.

 Patterns imitating the folds of the human brain are found in the aptly named Brain Coral taken off the Red Sea coast of Egypt in 2013.

Many animals show bilateral symmetry having a right and a left side and tropical fish are often beautifully patterned as this one from the Red Sea in Egypt.

  This is a desmid, a tiny alga from a local pond with two equal halves often patterned in themselves.

Merion Circulare: A diatom which likes to link up in colonies - this one making a circular pattern.

A salt crystal magnified 40 x. The basic cubic structure is visible here. Crystal shapes can be of many types.

Spherical bubbles tend to group together to make interesting patterns, The sphere has the smallest surface area for a given volume of any shape.

Tiny shells from a beach in North Wales show a spiral symmetry.

A sea urchin shell shows a five point symmetry

This insect eye shows spherical symmetry. A sphere of spheres.

 Patterns on the under wing of a Common Blue butterfly.

Swirling patterns on a soap bubble caused by interference of light by different thicknesses of film.

Pollen grains of the Common Mallow exhibit spherical symmetry.

Ripples on a pond. This rippling effect is similar to the patterns found in sand at the sea side and also dunes in the desert.

A Spider's web coated with ice crystals. Another of nature's intriguing patterns.

Fractal Art 4 - Mandelbulb3D

Mandelbulb3D is a free 3d fractal generating software program written by Jesse on FractalForums. Others in the group have contributed new formulae to produce an amazing application for generating fractal art. There are many formulae for different fractal objects to try each having parameters which can be tweaked. Formulae can be mixed and combined or hybriised to provide an infinite number of variations.

The 3D rendering environment includes lighting, color, specularity, depth-of-field, shadow- and glow- effects; allowing the user fine control over the imaging effects.

There is a 3d navigation pane which enables you to see the immediate effect of your changes on screen. I find it fairly intuitive to use. go to the following link to Download Mandelbulb3D.

I find the software great for creating sci fi art and you can add backdrops of starfields, galaxies or any jpg file you like.

Life in Glass Cases

Some of the most beautiful objects in the micro world can be found in the most humble of locations. look in any pond at the plants and rocks near the shoreline. Often they will be coated below the water with a brown scum like layer. If you scrape off a little of this brown scum into an airtight container you will almost certainly have collected hundreds if not thousands of these objects. What are these objects?  A look under the microscope will reveal  strange creatures which appear to live inside highly decorated and transparent cases, in many different shapes and sizes,

Such creatures really do exist, They are called diatoms and you can find them almost anywhere you find water. In fact they are so numerous that they produce at least 20% of the oxygen in the atmosphere. Diatoms are a type of Algae, microscopic in size and brownish in colour, and they get their energy from photosynthesis,

There are two main types of diatom:  centric , possessing radial or circular symmetry and pennate having bilateral symmetry ie two symmetrical halves  referring to their cases which are made of silica and transparent like glass.Some pennate diatoms move by forcing out water through a hole called a raphe. The cases are called frustules and are in two halves. They are perforated with tiny holes to enable waste to pass out and nutrients to flow in. The shapes of the cases and markings and striations are used to identify the different species of which there are many thousands.. Sizes range from 2 to 500 microns (0.5 millimetres).Diatoms can be solitary or linked in colonies in zig zag, side by side or star shaped formations.

Diatoms are fascinating to study under the microscope. They can have such intricate detail and varied shapes. I have found several species in a local stream attached to weeds and stone as a brownish scum.

A sample taken from a local stream. There are several species here of largely pennate diatoms. You can see many different shapes and at this relatively low magnification a glimpse of the ornamental detail of the silica cases. Most of the diatoms in this image are individuals.

Zooming in on a single diatom we can see the detailed striations of the silica case  while inside the golden brown of the living cell. The colour is due to photosynthetic pigments which harness light energy to produce energy rich substances.

  At higher magnifications intricate detail becomes visible. These pictures are approximately 400 x.

 A large pennate diatom.

 Many diatoms live in colonies. This one is attached corner to corner.


 These pennate diatoms are clustered around a filament of algae.

 These diatoms live in colonies attached to stalks.

 Fragilaria attached side by side.

Meridion Circulare.