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POHow can I reproduce a scribbly pattern like this in code?
 

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  1. POHow can I reproduce a scribbly pattern like this in code?
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    <p>I made this graph in wolfram alpha by accident:</p> <p><img src="https://i.stack.imgur.com/5elU2.gif" alt="Graph"></p> <p><strong>Can you write code to produce a larger version of this pattern?</strong></p> <p><strong>Can you make similar looking patterns?</strong> </p> <p>Readable code in any language is good, but something that can be run in a browser would be best (i.e. JavaScript / Canvas). If you write code in other languages, please include a screenshot.</p> <p>Notes:</p> <ul> <li>The input formula for the above image is: arg(sin(x+iy)) = sin^(-1)((sqrt(2) cos(x) sinh(y))/sqrt(cosh(2 y)-cos(2 x))) (<a href="http://www.wolframalpha.com/input/?i=arg%28sin%28x%2Biy%29%29+%3D+sin%5E%28-1%29%28%28sqrt%282%29+cos%28x%29+sinh%28y%29%29%2Fsqrt%28cosh%282+y%29-cos%282+x%29%29%29" rel="nofollow noreferrer">link</a>)</li> <li>You don't have to use to use the above formula. Anything which produces a similar result would be cool. But "reverse engineering" Wolfram Alpha would be best</li> <li>The two sides of the equation are equal (I think), So WA should have probably only returned 'true' instead of the graph</li> <li>The pattern is probably the result of rounding errors.</li> <li>I don't know if the pattern was generated by iterating over every pixel or if it's vector based (points and lines). My guess is with vector.</li> <li>I don't know what causes this type of pattern ('Rounding errors' is the best guess.)</li> <li>IEEE floating point standard does not say how sin or cos, etc should work, so trig functions vary between platforms and architectures.</li> <li>No brownian motion plots please</li> </ul> <p>Finally, here's another example which might help in your mission: (<a href="http://www.wolframalpha.com/input/?i=arg%28sin%28x%2Biy%29%29+%3D+tan%5E%28-1%29%28cot%28x%29+tanh%28y%29%29" rel="nofollow noreferrer">link</a>)</p> <p><img src="https://i.stack.imgur.com/BGp14.gif" alt="Graph 2"></p>
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    1. USQubei
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      1. POHow can I reproduce a scribbly pattern like this in code?
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      1. POHow can I reproduce a scribbly pattern like this in code?
      1. USStephane Rolland
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      1. POHow can I reproduce a scribbly pattern like this in code?
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    1. COyour problem with the equality holding only for certain ranges of x seems to be something related to multivalued functions. If you take Sin[] of both sides, your equality holds everywhere.
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      1. POHow can I reproduce a scribbly pattern like this in code?
      1. USDr. belisarius
 

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