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What is the slowest series of superlinear growth rates constructible in cgol? For clarification, a "series" of growth rates is any set of functions which can be represented as steps in an iterative function, and each O(n) should grow either faster or slower than the next. An example of such series is x, xlog(x), xlog(log(x)), Mandelbrot set (the function in particular is one of these), (x+a)^n, etc. My question is what cgol-constructible series of growth rates approaches O(n)=x fastest. So far I know of embedded logarithms, but there may be faster alternatives.
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x = 36, y = 28, rule = TripleLife 17.G$17.3G$20.G$19.2G11$9.EF$8.FG.GD$8.DGAGF$10.DGD5$2.2G$3.G30.2G$3G 25.2G5.G$G27.G.G.3G$21.2G7.G.G$21.2G7.2G!