• 0 Vote(s) - 0 Average
• 1
• 2
• 3
• 4
• 5
 How it looks (i.θ)ₐ marraco Fellow Posts: 93 Threads: 11 Joined: Apr 2011 04/18/2015, 11:20 PM (This post was last modified: 04/19/2015, 05:35 AM by marraco.) $\vspace{15}{e^{i.\theta}}$ is an interesting and important function, so what we get if we do the same with tetration: $\vspace{15}{^{i.\theta}a}$? I put i.x in the polynomials obtained by minimizing the error $\vspace{15}{\Delta^2 \,=\, (^{x}a-a^{^{x-1}a})^2}$, and drawed the imaginary vs real part: These functions probably are periodical, but my polynomials only converge on -1≤x≤1, so, be careful about looking at values outside of that range. For example, this chart is only valid in the range 0..4, for real and -4..3 for the imaginary axis. This is base $\vspace{15}{e^{-e}}$ This is base $\vspace{15}{e^{\frac{1}{e}}}$ This is a zoom in the curl transition base e, or something close, seems to delimit the transition towards the negative axis: Many of these seem to be described by something like $\vspace{15}{^{i.x}a\,=\,c+a.cos(n.x) \,+\, i. b.sin(m.x)}$ « Next Oldest | Next Newest »

 Messages In This Thread How it looks (i.θ)ₐ - by marraco - 04/18/2015, 11:20 PM RE: How it looks (i.θ)ₐ - by sheldonison - 04/19/2015, 02:40 PM RE: How it looks (i.θ)ₐ - by marraco - 04/19/2015, 08:40 PM RE: How it looks (i.θ)ₐ - by sheldonison - 04/19/2015, 11:19 PM RE: How it looks (i.θ)ₐ - by marraco - 04/20/2015, 02:35 AM RE: How it looks (i.θ)ₐ - by Gottfried - 04/20/2015, 07:53 AM RE: How it looks (i.θ)ₐ - by marraco - 04/21/2015, 02:34 AM RE: How it looks (i.θ)ₐ - by marraco - 04/21/2015, 03:20 AM RE: How it looks (i.θ)ₐ - by sheldonison - 04/21/2015, 08:23 AM RE: How it looks (i.θ)ₐ - by marraco - 04/23/2015, 04:52 PM RE: How it looks (i.θ)ₐ - by JmsNxn - 04/23/2015, 11:15 PM RE: How it looks (i.θ)ₐ - by sheldonison - 04/23/2015, 11:20 PM RE: How it looks (i.θ)ₐ - by marraco - 04/26/2015, 12:50 AM RE: How it looks (i.θ)ₐ - by sheldonison - 04/26/2015, 05:08 AM RE: How it looks (i.θ)ₐ - by marraco - 04/20/2015, 03:46 AM RE: How it looks (i.θ)ₐ - by marraco - 04/23/2015, 02:21 AM RE: How it looks (i.θ)ₐ - by marraco - 04/25/2015, 07:52 PM

Users browsing this thread: 1 Guest(s)