[FRIAM] Fractal discussion Landscape-bird songs

[Jon Zingale]

Glen,

Thank you for the cool image and for
diving into the code. To answer your
question, I am using Euler's method to
compute the trajectories of the Lorenz
equations. `Eball` denotes the step size
of the integration. In theory, making the
Eball param smaller ought give better
numerical solutions while increasing
ought give less accurate solutions.

Takens' method, seems to rely heavily on an
appropriate choice of delay time. I utilize a
BBD <https://en.wikipedia.org/wiki/Bucket-brigade_device> style delay line,
@delay in code.

In my investigations so far, a step size of 0.003
seems best paired with a delay of 30 steps. A
step size of 0.009 seems to benefit from a shorter
delay of 10 steps. Decreasing the step size to
0.0009,  I have been able to increase delay times
to 100 steps with satisfying result.

I suspect that by weakening the accuracy of the
integration, longer delay times force Takens' method
to rely on less accurate information and the
reconstruction suffers. I am open to additional
thoughts and theories.

Cheers,
Jon
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