• Hjalmar@feddit.nu
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      10 months ago

      I have so many questions about that freaking creature. Can it partially unfold to reach anything arbitrarily far away? And how would it go about washing it’s infinite surface area?

      • wolf_2202
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        10 months ago

        That depends on the decay factor of one centaur to the next. If the centaurs shrink by anything more than a factor of two, then no. The creature will converge onto a single length.

        • Liz@midwest.social
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          10 months ago

          What? If it’s geometric it needs to be less than 1, that’s all. 9/10 + 81/100 + 729/1000 + … = 10

          C•(1-r)-1 = C•x

          Where r is the ratio between successive terms.

        • eestileib
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          10 months ago

          Should be anything less than a harmonic decrease (that is, the nth centaur is 1/n the size of the original).

          The harmonic series is the slowest-diverging series.

          • Kogasa@programming.dev
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            10 months ago

            The assumption is that the size decreases geometrically, which is reasonable for this kind of self similarity. You can’t just say “less than harmonic” though, I mean 1/(2n) is “slower”.

            • eestileib
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              10 months ago

              Eh, that’s just 1/2 of the harmonic sum, which diverges.

              • Kogasa@programming.dev
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                10 months ago

                Yes, but it proves that termwise comparison with the harmonic series isn’t sufficient to tell if a series diverges.

                • eestileib
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                  10 months ago

                  Very well, today I accede to your superior pedantry.

                  But one day I shall return!

        • Hjalmar@feddit.nu
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          10 months ago

          Judging by the image the centaura shrink with about a factor of two so the entire creature should be either infinitely long or just very very long.