Is the "temperature" simply the maximum distance from the origin? Can you say more about the dependence on the number of steps? Is it possible that we would see a higher temperature for e×γ if we let it go longer? Why the insistence that the turn increment be irrational? Is it the existence of repeating regimes that just march steadily away from the origin? As the turn increment decreases toward zero, doesn't the very first excursion extend arbitrarily far, like an infinite New-Year's-Eve noisemaker unfurling? Or did I misunderstand a definition? On Wed, Feb 21, 2018 at 3:35 PM, Ed Pegg Jr <ed@mathpuzzle.com> wrote:
For six years, the product of the two Euler constants e×γ has given the highest temperature in the Curlique fractal. The value e×γ has a temperature of 2433.73 at 460024 steps.
We have a new record. https://math.stackexchange.com/questions/69303/
The fundamental unit of the Calabi Triangle ratio, x^3+x^2−7x+1=0 with x≈2.10278... , has a temperature of 4408.7 after 2005399 steps.
Can anyone get a higher temperature?
--Ed Pegg Jr _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun