This is the domain coloring of Riemann zeta function. I do get the Re(z) < 1 part of the graph. However I am unsure why the Re(z) > 1 part of the graph is all red with the same brightness and hue. Why is this so?
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$\begingroup$ It simply depends on the coloring chosen. For your picture above it was most probably the following coloring as your plot is also from wikipedia: de.wikipedia.org/wiki/Riemannsche_%CE%B6-Funktion#/media/… $\endgroup$– YukiJCommented Aug 30, 2018 at 11:08
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$\begingroup$ @YukiJ Yes, but shouldn't the red color get fainter as ||z|| gets bigger? $\endgroup$– DimenCommented Aug 30, 2018 at 11:10
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2$\begingroup$ Check the x-axis of the plot. It ranges to 40 in your plot only. The coloring above starts fading for slightly bigger values than that. $\endgroup$– YukiJCommented Aug 30, 2018 at 11:13
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$\begingroup$ @YukiJ Oh I forgot to check the range! Thank you (*'▽') $\endgroup$– DimenCommented Aug 30, 2018 at 11:15
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$\begingroup$ You could get a better understanding and perspective with this youtube video, > Visualizing the Riemann Zeta function. : youtube.com/watch?v=sD0NjbwqlYw $\endgroup$– JustinCommented Aug 30, 2018 at 11:29
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1 Answer
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Just to put my comments into a coherent form and answer:
The way the graph looks like depends on the coloring chosen. For your picture above it was most probably this coloring since your plot is also from wikipedia.
You will notice that the graph of the zeta function in your question is only depicted for values up to 40 on the $x$-axis. The coloring, however, starts changing for slightly bigger values than that only. So, in this domain the whole right side is red. If you plotted the zeta-function for values up to say 150 on the right you would see several differences. I hope this clarifies it.
