Unexpected and idiosyncratic failures to converge

[RoyWiggins]

I have been using this code to map the interior of the Koch snowflake. This is my most successful, but the algorithm seems to fail on very similar polygons.

If I make my snowflake slightly spikier, it just fails entirely:

And if I iterate the snowflake one more time, it pretty much always fails.

This is not, I believe, a fundamental problem with the Zipper algorithm, as I was able to render a higher iteration snowflake using the FORTRAN implementation that Marshall has provided. It's a lot harder to work with his implementation though, so I had hoped that I'd be able to use it in Julia instead.

I don't suppose you have any ideas what might be going wrong?

[RoyWiggins]

a test case using my fork that works in julia 1.0

[sswatson]

Thanks for working to convert this package to Julia 1.0.

You'll find that you can get your example to work with k = 0.9 if you use BigFloats instead of Float64s. Of course, this is much slower, but depending on your situation, you might find the speed acceptable.

Given that the Fortran code does not have this problem, I suspect that I'm using an unstable arithmetic operation somewhere (like subtracting two very close numbers). If I figure it out, I will follow up on this thread.

[RoyWiggins]

My update for Julia 1.0 seemed to work- I just took the automatic updates suggested by Julia's upgrade-bot. I'm very new to Julia so my understanding of how Julia deals with modules/packaging is rudimentary.

BigFloat does indeed work great. We'll see how the speed goes... I'm hoping to calculate the map to the circle to a high resolution so I can paint things onto the circle and color the snowflake with it. Depending on exactly how long that ends up taking, it could well be just fine, since once it's calculated for a given resolution I won't need to do it again.

[RoyWiggins]

I ended up finding a test case. This triangle works:

vertices = [
    -.5  -1;
    1  -1;
    -.5  1.; 
]
f = ConformalMap(vertices,-.25)
visualize(f)

And this one explodes:

vertices = [
     1  -1;
     -.5  1.; 
     -.5  -1;
]
f = ConformalMap(vertices,-.25)
visualize(f)

They're exactly the same triangle, but with the vertices rotated around.

[copyrite]

Hi,
First of all I've been working on a MATLAB implementation of Zipper and @sswatson's ConformalMaps has been very helpful to study. I happened to test my implementation on various Koch snowflakes, and on fourth generation or so the forward map started to fail on certain configurations. The slit algorithm exhibits similar problems. So it's probably not (just) the algorithm.