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

Question

I made this graph in wolfram alpha by accident:

Can you write code to produce a larger version of this pattern?

Can you make similar looking patterns?

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.

Notes:

• 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))) (link)
• 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
• The two sides of the equation are equal (I think), So WA should have probably only returned 'true' instead of the graph
• The pattern is probably the result of rounding errors.
• 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.
• I don't know what causes this type of pattern ('Rounding errors' is the best guess.)
• IEEE floating point standard does not say how sin or cos, etc should work, so trig functions vary between platforms and architectures.
• No brownian motion plots please

Finally, here's another example which might help in your mission: (link)

Answer 1

As you asked for similar looking patterns in any language, here is the Mathematica code (really easy since Wolfram Alpha is based on Mathematica)

Edit

It is indeed a roundoff effect:

If we set:

and make a plot

Plot3D[f[x, y], {x, 7, 9}, {y, -8, -9},WorkingPrecision -> MachinePrecision]

The result is:

But if we extend the precision of the plot to 30 digits:

Plot3D[f[x, y], {x, 7, 9}, {y, -8, -9},WorkingPrecision -> 30]  

We get

and the roughness is gone (which caused your scribbly pattern)

BTW, your f[x,y] is a very nice function:

So if I managed to copy your formulas without errors (which should be considered a miracle), both sides of your equation are equal only in certain periodic ranges in x, probably of the form [2 n Pi, (2 n + 1) Pi]