Conclusion
The conceived fractal has a volume of 65 625∏ cubed units and an area of 25 312,5∏ squared units.
Extension possibilities
- To better replicate human lungs, the addition of one cylinder per each iteration at (36o/n) degrees would be suitable. Such a model, created with programmation in a software such as OpenSCAD, could create a much more accurate fractal and, with the introduction of loops in the program, ensure self-similarity. The model could then be used to calculate the pressure in the lungs at a given time, by applying the formula P=F/A, where the surface area is known from the programmed model, and the force is an approximated function or constant that varies between systolic and dyastolic pressure.
- By rotating the fractal at 180 degrees on a vertical plane, the iterated part of the fractal resembles the canopy of a tall decidious tree, such as a maple, a linden or a cottonwood tree. To better fit the shape of a tree, however, three secondary branches instead of two should originate from the main trunk, at 120 degrees from one another on a horizontal plane. The radius of the branches would also decrease faster along a x/4 fashion
- An inverted lung pattern, in which the iterated part is directed upwards, in which each branch divides in two, gives rise to a seaweed pattern.
Each of these avenues of reasearch are possible by tinkering slightly the present model and iterating it further.
