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can someone please identify the fault here, i cant find it
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take natural logarithm of both sides
Complex logarithms are not unique - you'd normally take the principle value; that is the value of ln(z) = ln|z| + i x arg(z) when arg(z) is taken to be the principle argument of z. In this case, another value has been taken, so the equality gained by taking logarithms does not hold.
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i get it now, i do remember when plotting the natural logarithm over the complex plane that it did create, what might resemble a black hole creating a hole in space time
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luca - could you maybe post that? I'd like to see it
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ill make up a quick app to graph it again, i long ago lost it
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Thanks in advance
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well i started building a scan line renderer to render the graph, then realised i couldnt be bothered, but also that wolfram has a graph of it
http://mathworld.wolfram.com/images/interactive/NaturalLogReImAbs.gif
i refer to the top left one of cause, y = re[ ln(x+zi) ]
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Neat, thanks for finding the link
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i decided to do it anyways
the colour is a function of y, perspective correct interpolation over the triangle to give the smooth colouring, it is estimated with 100 points from x,z = -5 -> 5 with a cap on y from -2 to 4
http://denvish.net/ulf/1169681050_comp.php
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heres another rendering, this time with 16x the number of triangles, you can see a few visual artifacts, but otherwise its much nicer than previous rendering
and no, these are not pre rendered, its procedural
http://denvish.net/ulf/1169681454_comp.php
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this one is a bit cooler in my opinion, obviously the rendering size has dropped down, and the polygon count has also dropped back down to original, but it does run pretty fast considering its now real time rendering rather than a single rendering.
http://denvish.net/ulf/1169709520_comp.php
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