ART MATRIX PO 880 Ithaca, NY 14851-0880 USA (607) 277-0959, Fax (607) 277-8913 'The Paths of Lovers Cross in the Line of Duty.' THE THEORY BEHIND 'THE CELL AND THE WOMB' Mandelbrot and Julia Survivability Maps. Copyright (C) 1988 Homer Wilson Smith Consider the Planet Earth. It consists of many climates and terrains where various things may or may not grow depending on the hospitality of the environment to the item in question. Let us consider the case of simple American Corn. Let's do the following thought experiment. Place a grid over every square foot of the Planet Earth so that every square foot is clearly demarked. This grid covers oceans and mountains and deserts and fertile ground alike. Plant one seed of corn in each and every square foot whether it be under water or on mountain top or on fertile soil. You don't have to do this all on the same day, but eventually you will have to study every square foot of the planet in this fashion. After the seeds have been planted, come back to each square foot every day and record if the planted corn is still growing and viable. If it is, let it be. If however the seed has failed to grow or has died then mark that square with the number of days the corn managed to stay alive before it died. After every square foot of Earth has been mapped in this manner, color each square foot according to the number marked in it. Color the numbers according to the simple rainbow starting at red and continuing through yellow, green, cyan, blue and magenta. Where the numbers are small, meaning the corn died quickly assign the red end of the spectrum. Where the numbers are large meaning the corn lasted for a long time and maybe even went a few generations before dying assign the magenta end of the spectrum. For values inbetween the two extremes assign the colors in the middle of the spectrum in an even distribution. Where the corn is still growing at the end of the experiment color it black. This is a Mandelbrot Survivability Map. The map represents all the different possible ENVIRONMENTS the corn could be planted in. The color represents how long the corn survived before it died. The black areas represents where the corn survived best and is indeed still growing. The reason we are giving DEATH such importance here, by coloring it, is because death is what distinguishes one square foot from another. If two different squares both have corn still living in them, they can not be distinguished from each other. Both are still alive. But if one or both dies, then they can be distinguished by WHEN they died. It is the change in state that causes the discrimination to take place. The corn starts out alive (as a seed). If it ends up still alive then no change has taken place. But if it dies then that is a significant change which we record as a color demarking it as different from its neighbors. Now let's change the experiment. This time we collect together one seed of every known edible vegetable on Earth. This of course would include the corn used above. We pick just one particular square foot of Earth from the above Mandelbrot Survivability Map. It does not matter whether that square foot is a colored one or not, but for our first experiment let's pick a black square foot. This guarantees that at least something will grow there, namely our corn seed. We then plant each one of our seed collection in that one square foot of Earth. We do not plant them all at the same time, but rather we plant each in turn and let it grow and see what happens. Then we repeat the experiment with the next seed in line and so on until all seeds have been planted and been allowed to grow and die (or live). For each seed we keep a record of how long it survived in that particular square foot of Earth. If a seed seems to grow forever though we cut the experiment short at some reasonable arbitrary time so that we have time to finish the rest of the experiment with the other seeds. After all of our seeds have been allowed to grow and die in our single plot of land, we arrange them in a square grid on a table (a very large table!). We mark on the table the number of days the seed managed to survive before it died or was cut short by the need to get on with the other seeds. We then color the table with the same method used in the Mandelbrot case. Those positions on the table having small numbers in them get the red end of the spectrum. This means they died quickly in this one plot of land. Those having large numbers get the magenta end of the spectrum, and those inbetween get all the other colors between red and magenta. Where the seeds survived so long they had to be cut short, color the table black. Thus you have a Julia Survivability Map. A Julia Map represents every possible item that could grow in ONE PARTICULAR environment and how long it was able to survive there. Clearly a Julia Survivability Map could be made for every square foot on Earth planting all the seeds for all the vegetables in each square foot just like we did for the first square foot. Thus each and every point in the Mandelbrot Survivability Map has a complete Julia Survivability Map associated with it. In terms of knowledge, what is gained from these two types of maps is a thorough knowledge of what grows where. Pretty important don't you think? Defining some terms here, let's call the starting seeds ENTITIES and the square of land they are planted in the ENVIRONMENT. If the entities can be called INSIDES then the environments can be called OUTSIDES. A Mandelbrot Map is a picture of every possible ENVIRONMENT one seed or entity could be planted in and it is colored according to how how well that one entity survived in each different environment. It records how well one starting INSIDE does in every possible OUTSIDE. A Mandelbrot Survivability Map can be made for any INSIDE of interest and shows how well that one INSIDE survived in all possible OUTSIDES in existance. A Julia Survivability Map is a picture of every possible SEED or ENTITY that could be planted in just one chosen ENVIRONMENT, and each different SEED is colored according to how well it survived in that one chosen environment. It records how well every possible INSIDE survives in one possible OUTSIDE. A Julia Survivability Map can be made for any single OUTSIDE of interest and shows how well all possible INSIDES in existance survived in that one chosen OUTSIDE. With a complete set of Mandelbrot and Julia Survivability Maps for all the food on Earth and all the places you could plant it, you would have a complete directory of what grew where and how well. Nothing new and no big deal. Its just a way of looking at it.