imported>Caesar Schinas |
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| == Summary == | | == Summary == |
| {{Image_notes_ownwork2
| | Importing file |
| |Description =Funciton <math>~f=\ln(z)~</math> in the complex <math>~z~</math>-plane.<br>
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| Abscissa is <math>~\Re(z)~</math>,
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| Ordinata is <math>~\Im(z)~</math>. <br>
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| lines of constant <math>~\Re(f)~</math> and
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| lines of constant <math>~\Im(f)~</math> are shown.<br>
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| Level <math>~\Im(f)=-2~</math> and
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| level <math>~\Im(f)=-1~</math> are shown with thick red lines.<br>
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| Level <math>~\Im(f)=1~</math> and
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| level <math>~\Im(f)=2~</math> are shown with thick blue lines.<br>
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| Levels<br>
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| <math>~\Im(f)=0~</math> ,<br>
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| <math>~\Re(f)=-2~</math> ,<br>
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| <math>~\Re(f)=-1~</math> ,<br>
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| <math>~\Re(f)=0~</math> ,<br>
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| <math>~\Re(f)=1~</math> ,<br>
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| <math>~\Re(f)=2~</math> ,<br>
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| are also shown with thick black lines.<br>
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| Intermediate levels are shown with lines:<br>
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| green is used for <math>~\Im(f)~=\rm const~</math> ,<br>
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| red is used for <math>~\Re(f)~=\rm const < 0~</math> ,<br>
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| blue is used for <math>~\Im(f)~=\rm const > 0~</math> . <br>
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| The cut at <math>~z<0~</math> is shown with multicolored line.<br>
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| Gridlines are drawn with unity interval and cover the range<br>
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| <math>~-4\le \Re(z)\le 16~</math> ,<br>
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| <math>~-4\le \Im(z)\le 4~</math> . <br>
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| |Year_created =2008
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| |CZ_username = [[User:Dmitrii Kouznetsov|Dmitrii Kouznetsov]]
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| |Notes = Free use is granted. You may copy, distribute, even modify.
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| If you have mathematica software installed, I can even send you the source.
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| From my opinion, the figure is trivial: just straight lines circles and mesh.
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| However, it the [[black square]] and [[black circle]] by [[Malevich]] are considered as art, you could consider this logarithm as a shedevr of computer graphics.. Anyway, I release this work to the public property. If you think that the copyleft license is not filled as follows, I authorize you to correct it according to the statement above.
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| |Other_versions =http://commons.wikimedia.org/wiki/Image:Logez02.jpg
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| }}
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| == Licensing/Copyright status ==
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| {{CC|by|3.0}}
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