Pentatri

The pentatri is equal to {3,3,3,3,3}, 3 metapowerexploded 3, or {3,5 (1) 2} in BEAF.

{3,3,3,3,3}

= {3,{3,2,3,3,3},2,3,3}

= {3,{3,3,2,3,3},2,3,3}

= {3,{3,{3,2,2,3,3},1,3,3},2,3,3}

= {3,{3,{3,3,1,3,3},1,3,3},2,3,3}

= {3,{3,{3,3,{3,2,1,3,3},2,3},1,3,3},2,3,3}

= {3,{3,{3,3,{3,3,3,2,3},2,3},1,3,3},2,3,3}

= {3,{3,{3,3,{3,{3,2,3,2,3},2,2,3},2,3},1,3,3},2,3,3}

= {3,{3,{3,3,{3,{3,3,2,2,3},2,2,3},2,3},1,3,3},2,3,3}

= {3,{3,{3,3,{3,{3,{3,2,2,2,3},1,2,3},2,2,3},2,3},1,3,3},2,3,3}

= {3,{3,{3,3,{3,{3,{3,3,1,2,3},1,2,3},2,2,3},2,3},1,3,3},2,3,3}

= {3,{3,{3,3,{3,{3,{3,3,{3,2,1,2,3},1,3},1,2,3},2,2,3},2,3},1,3,3},2,3,3}

= {3,{3,{3,3,{3,{3,{3,3,{3,3,3,1,3},1,3},1,2,3},2,2,3},2,3},1,3,3},2,3,3}

= {3,{3,{3,3,{3,{3,{3,3,{3,{3,2,3,1,3},2,1,3},1,3},1,2,3},2,2,3},2,3},1,3,3},2,3,3}

= {3,{3,{3,3,{3,{3,{3,3,{3,{3,3,2,1,3},2,1,3},1,3},1,2,3},2,2,3},2,3},1,3,3},2,3,3}

= {3,{3,{3,3,{3,{3,{3,3,{3,{3,{3,2,2,1,3},1,1,3},2,1,3},1,3},1,2,3},2,2,3},2,3},1,3,3},2,3,3}

= {3,{3,{3,3,{3,{3,{3,3,{3,{3,{3,3,1,1,3},1,1,3},2,1,3},1,3},1,2,3},2,2,3},2,3},1,3,3},2,3,3}

= {3,{3,{3,3,{3,{3,{3,3,{3,{3,{3,3,3,{3,2,1,1,3},2},1,1,3},2,1,3},1,3},1,2,3},2,2,3},2,3},1,3,3},2,3,3}

= {3,{3,{3,3,{3,{3,{3,3,{3,{3,{3,3,3,{3,3,3,3,2},2},1,1,3},2,1,3},1,3},1,2,3},2,2,3},2,3},1,3,3},2,3,3} NOOOOOOOOOOOOOOOOOOOO!!!!!!!!!!!

tetratri is much much much smaller than pentatri

= {3,{3,{3,3,{3,{3,{3,3,{3,{3,{3,3,3,{3,{3,{3,3,{3,{3,{3,3,{3,{3,{3,3,3,tetratri},1,1,2},2,1,2},1,2},1,2,2},2,2,2},2,2},1,3,2},2,3,2},2},1,1,3},2,1,3},1,3},1,2,3},2,2,3},2,3},1,3,3},2,3,3} YIKES!!!

Let's have a function G where G = 3, GG = 33, this is tetratri, GGG = 33, with tetratri sets of {}, Go to GGGGGGGGGGGGGG..............GGG G's...............GGGGGGGGGGGGGG, this is {3,3,2,1,2}

GG G = {3,3,2,1,2}

GG G G G ... G G      (GG G G's) = {3,3,3,1,2} = G^^^3

G^^^^3 = {3,3,4,1,2}, G^^^^^3 = {3,3,5,1,2}, G^^^^^^3 = {3,3,6,1,2}, G^^^^^^^^......G^^^G ^'s......^^^^^G = {3,3,1,2,2}

GG = {3,3,3,2,2}

GG = {3,3,3,3,2}

GG with GG sets of {}, This is {3,3,{3,3,3,3,2},2,2} = {3,3,3,{3,2,1,1,3},2} = {3,3,1,1,3}, we are now breaking past the G function! We need a new function, call it H. H = G, HH = GG, HHH = GG with GG sets of {}, we can now describe {3,3,1,1,3} as HHH or H^3. You probably see the pattern.

H^^H = {3,3,2,1,3}

H^^^H = {3,3,3,1,3}

H^^^^^^......H^^^H ^'s......^^^^^^^H = {3,3,1,2,3}

H^^^^^^......H^^^^^^^ ......H^^^H ^'s......^^^^^^^H ^'s...... ^^^^^^^H = {3,4,1,2,3} This is {3,3,1,2,3} levels of recursion past the H function.

H{n}H = n levels of recursion past the H function, {3,3,n,1,3}

HH = {3,3,n,2,3}

HH = {3,3,n,3,3}, make n=3, this is pentatri