A lecture to be presented in Costa Rica, August 2004

previous patterns class here

Patterns of Nature

These are activities to accompany the book Patterns in Nature by Pat Murphy.
I was a science adviser for this book, Paul Doherty.

Images from My collection, from Amy and explo site.

Copies of articles from Exploring (to Ale for translation?)


Ic cave hand print, Antarctica.

Straight Lines

These rays of sunlight and shadow are really parallel, yet from our point of view they look radial.

Crepuscular Rays, rays of sunlight made by distant towering clouds.

Looking down from an airplane at the rays of sunlight.

All mountain shadows are triangular.


Spirals and Helices

Images of plant spirals, shell spirals snails and seashells

Demo Overhead Making an archimedean spiral of rope.
Coil a rope in a flat spiral. Each turn is one rope width further from the center.
Coil rope on a boat.


The logarithmic spiral of a seashell.

Making a logarithmic spiral with rope. This makes a shape like a nautilus shell.

Fibonacci, many plants have Fibonacci numbers of spirals.

Fibonacci Bees, count the ancestors of a male bee and find the Fibonacci series. Illustration.

A mathematician builds a plant, place the leaves to minimize shading.

Counting Plant Fibonacci 1 Count the spirals in pine cones, pineapples,and sunflowers
Modeling Plant Fibonacci 2 Model these spirals

Helices, spirals in 3-D

Trees in the mountains often grow with a spiral twist to make them stronger when they bend in the wind.

Water going down the drain makes a vortex with spiral ridges along its sides.
This vortex was made by a leak in the May Lake dam in Yosemite National Park.

Demo Fill a 2 liter bottle with water. Swirl it around, invert the bottle, watch the spiral vortex develop as the water swirls out of the bottle.


Images of river meanders.

Entrenched meander near meteor crater Arizona.

An incised meander.


Demo Overhead Bend metal or plastic straps to make the sine-generated curve of river meanders.

Ice balloons Fill a balloon with water. Place it in a freezer overnight to make an ice balloon. Sprinkle salt on the top of the ice balloon. Salt melts the ice and the resulting water carves meandering channels as it flows down the surface.

Looking at an ice balloon.

Salt water carves meanders as it flows down the surface of the ice balloon.


Images ripple marks, waves

Ripples in water reflecting sunlight.

Water capillary waves

Interference of water waves.

Water waves reflecting ttrees.

Demo Wave activities, on a phonecord or slinky, waves in water, ripple marks. Ripple marks on Mars.



Water Drops

Dew Drops on a spider web are spherical, until they become too large and become deformed by gravity.

Water drops on leaves. The leaves are coated with hydrophobic, "water fearing" waxy hairs.

Water drop lenses. These are not spheres they have flat bottoms.

Soap Bubbles

Soap bubbles are also spheres when they are small. The gas inside is separated from the surrounding air by a thin spherical layer of soapy water. Recently astronauts on the space shuttle managed to make bubbles from pure water, water without soap.

Soap bubbles are also spheres.

A frozen soap bubble. A soap bubble touching dry ice.

Circles made by spheres

Spherical raindrops carve a random array of circular arcs into a muddy surface.

Fossil raindrop prints show that it rained millions of years ago.


Spherical raindrops refract and reflect sunlight to make the circular arc of a rainbow or a fogbow.

A fogbow is colorless white due to the spreading of the colors of light by diffraction.

Small spherical waterdrops make colorful circles of a glory surround the shadow of an airplane and its contrail.

Non-circular ice crystals can still make circles in the sky.

Hexagonal prisms and plates of ice refract sunlight into a circular halo about the sun. It is the random distribution of the orientations of the prisms around all possible orientations within a circle that creates the circle..



When the hexagonal prisms are oriented, the resulting pattern in the sky becomes non-cicular. Known a sundog.


Lichens form concentric circular arcs on rock.

Concretions are spheres that grow inside of rocks.

Plant dissection, cut apart plants and search for patterns, Activity from The Science Explorer.

Strolling Among Flowers, Exploring Article by Maurice Bazin

Demo Right-left, explore a mirror and find out what it reverses.

Demo Right-Left beginning, explore the nature of right and left using rubber gloves.

Demo Mirrors Right-Left advanced test your understanding of right and left using a flat mirror, a curved mirror and a parabolic mirror.


Images branching of trees, roots, blood, lung, streams

Find the shortest network joining points.

Count the order of the branches of a stream.

See You're Retina, An amazing branching pattern you've been looking through and not seeing all your life.


Demo Overhead Packing identical balls, place spherical balls all the same size in a shallow bowl and observe how they pack together.

Beehive cell packing.

Hexagonal closest packing in a beehive.

Demo Overhead Floating Aluminum Coin packing, float aluminum coins in a tray of water and observe how they pack together.

Ice crystal shapes

A single six armed snowflake growing on a cobweb.

Giant ice crystal as big as my hand.

Feldspar crystals are rectangular in granite.


Demo Overhead CD in a microwave, place a CD in a microwave, turn on the power for 2 seconds or so and observe the pattern etched into the metal by electrical discharges.

Mud in a tray on a warm plate. Heat a thin layer of muddy clay in a shallow pan over a warm plate. Watch it dry out and crack.

When clay-rich mud dries it shrinks and cracks.
Notice how the newer thinner cracks join the older wider cracks at right angles.

Mudcracks form as the mud dries.

Image Columnar Basalt, mud cracks

Fractured volcanic rock of Devil's Tower Wyoming.

Frost Polygons in Antarctica.


Bubbles in a bottle, fill a bottle with bubble solution, pour it out and the bottle fills with bubbles. Notice the bubble patterns.

Bubbles in a CD jewel box

Bubbles in 3-D, Snackbook

Bubbles on a tray, make 2,3,4 which define a plane, line and point at their intersection. Amy Images. Also large bubble versus small.

Bubble prints : The Science Explorer Bubble Prints Activity, Use dye colored soap bubbles to print bubble patterns onto paper.


The fractal pattern in a cone shell.

The fractal pattern in a fern-like mineral.

Demo Overhead Paint fractals Make a fractal pattern on plastic using enamel paint.

Fractals in Nature, Exploring Article, The Practical Fractal, Mary Miller

Demo Bifurcation, drip food coloring into water.




Scientific Explorations with Paul Doherty

© 2004

27 May 2004