DrakeEQ vs G^N

Are we alone? We created DrakeEQ to provide a visually elegant answer to the extraterrestrial question, using the intellectually elegant Drake Equation. We coupled this fun calculator with beautiful, 3D galaxies in motion! To help us celebrate 15 years since the first release in 2009, DrakeEQ 7.0.0 now features our Galaxene Galaxy Engine! Use this fun simulator to graphically quantify the number of advanced extraterrestrial civilizations in our Milky Way Galaxy. Travel the Universe and explore infinitely variable galaxies! Just pinch anywhere and tap the targeting indicator. Perform thought experiments with this unique visual tool; it’s both educational and entertaining. Learn about the famous Drake Equation through direct manipulation of its 7 parameters with DrakeEQ. The Drake Equation states that: N = the number of civilizations in our galaxy with which communication might be possible where: R* = the average rate of star formation in our galaxy fp = the fraction of those stars that have planets ne = the average number of planets that can potentially support life per star that has planets fℓ = the fraction of the above that actually go on to develop life at some point fi = the fraction of the above that actually go on to develop intelligent life fc = the fraction of civilizations that develop a technology that releases detectable signs of their existence into space L = the length of time such civilizations release detectable signals into space. Drake Equation. Wikipedia, The Free Encyclopedia.

G^N is a special calculator not just a game: This math app animates iterations of one or compositions of two multi-valued maps for free groups of in principle arbitrary finite rank in the abelian and non-commutative cases respectively (in this version the rank is restricted to values in between 2 and 11). Well-known examples of such multi-valued maps are permutations, for example the flip (x_1,x_2)->(x_2,x_1), in G^N we just write (1,2)->(2,1) and instead of the inverse we convenient flip the number. A more involved type of such a multi-valued map is the n+1 cycle defined by (1,...,n)->(-2-3-...-n-1,3,4,...,n,1), a non-trivial theorem. For example if n=2 this map is the hexagon (1,2)->(-2-1,1), this map applied twice reads (1,2)->(2,-2-1) and the third iteration is the identity map (1,2)->(1,2).