Branching in Nature Hands-On Investigations and Activities

1. Branching in Nature Hands-On Investigations and Activities

2. Investigation of Physical Branching • Viscous branching results from the interaction of two fluids of different viscosities. • Crème fraiche on top of squash soup at the Monkey Bar in Amherst, MA.

3. Hele Shaw Cell • Get two clear halves of a CD case • Drill a hole in the center of one case • Put one half down on a surface with the flat surface facing up • Put two thin pieces of glass along two edges of the plastic • Pour the first viscous fluid to be tested into the middle of the plastic bottom • Put the plastic half with the hole in it on top, flat surface facing down. • Inject the second viscous fluid to be tested into the hole. • Experiment by changing the fluids, and changing the force of injection • Develop hypotheses about the interaction of various fluids. Test your hypotheses. • Can you quantify what you see?

4. One half of clear CD case

5. Hole drilled in the middle of another half of a clear CD case

6. Fluid to be tested is put in the center of the bottom half. Put two coverslips on both sides of the fluid at the edges of the plastic.

7. Put the top half down on the fluid with the smooth side facing down.

8. Wipe off the excess fluid which emerges from the hole

9. Fill a syringe with 3 ml of colored water

10. Place the syringe over the hole on the cell

11. Inject the colored water

12. Observe the results! Predict and test branching patterns from different fluids and different forces.

13. Investigation of Biological Branching • George Johnson, in his New York Times article entitled Of Mice And Elephants: A Matter Of Scale , states: • "scaling emerges from the geometrical properties of the internal networks animals and plants use to distribute nutrients ". Scaling laws arise from a network transport system where (1) a space filling hierarchical branching pattern is required (2) the final branch of the network (where nutrients are exchanged) is a size-invariant unit and (3) organisms have evolved so that the energy required to sustain them is minimized. These networks are fractal -- each small part is a copy of the whole. Scaling laws result from the interplay between the physical and geometric constraints implicit in these three principles. • There is a correlation between the power law model and much of the processes and shapes that define patterns in nature. It is a consistency that is driven by a both interdependency and feedback. • The scale invariant characteristics that are so prevalent in patterns in nature apparently serve to cope with environmental factors that are not scale invariant. These non-scalable factors (those that do not depend on body size, shape, magnification, or symmetry) include physical and chemical constants and water – the universal solvent for life which has non-scalable properties. • http://www.patternsinnature.org/pin_essay_01.html

14. Rhizometer • A rhizometer can be made by putting growing media into a sandwich or quart bag • Plant a seed as per directions on the seed package • Flatten the growing media • Sandwich the bag between two pieces of cardboard and clamp together with two binder clips • Observe undisturbed root growth over time by opening the chamber