"jr" <cre### [at] gmailcom> wrote:

> plane with "Honeycomb" pattern, seen through "kaleidoscope".

Wheee!   Nice job.  :)

Can you adjust the symmetry?  Have 6-fold, or 7?

After playing with this stuff a bit, it seems like that whole sin*cos xy yz zx
thing has a lot of potential as a base pattern to do all sorts of interesting
things with.  Even just the threshold can change the apparent look quite a bit.
And then you have the orthogonal plane value/slice to vary.

We can square the whole sum, square the terms, take the root, etc.

- BW

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hi,

"Bald Eagle" <cre### [at] netscapenet> wrote:
> ...
> Wheee!   Nice job.  :)

start on.  :-)


> Can you adjust the symmetry?  Have 6-fold, or 7?
> After playing with this stuff a bit, it seems like that whole sin*cos xy yz zx
> thing has a lot of potential as a base pattern to do all sorts of interesting
> things with.  Even just the threshold can change the apparent look quite a bit.

yes, I just discovered that replacing "tau" with "pi * scale_factor" and using
slightly different factors, things get real .. interesting.

re your question, I answer with an Obama quote: "Yes, we can" :-)  below is
excerpted from my WIP code:

/* added bailout & max_trace */
global_settings {adc_bailout (1/254) assumed_gamma 1 max_trace_level 255}

/* #mirrors */
#declare n_ = 3;

#declare angle_ = 360 / n_;

/* epsilon */
#declare eps_ = 1e-3;

/* length of tube */
#declare len_ = 10;

/* prism with hole */
#declare pi_ = <.99,0,0>;
#declare po_ = <1.01,0,0>;

#declare pts_ = array [n_][2];

#for (i_, 0, n_-1)
  #local ta_ = vrotate(po_, <0,(angle_*i_),0>);
  #local tb_ = vrotate(pi_, <0,(angle_*i_),0>);
  #local pts_[i_][0] = <ta_.x,ta_.z>;
  #local pts_[i_][1] = <tb_.x,tb_.z>;
#end

/* rotate to centre on -z */
prism {
  linear_spline eps_, len_, 2*(1+n_),
  #for (i_,n_-1,0,-1) pts_[i_][0], #end pts_[n_-1][0],
  #for (i_,0,n_-1) pts_[i_][1], #end pts_[0][1]
  open
  sturm on
  no_shadow
  finish {ambient 0 reflection {1} specular 0}
  rotate <270,0,0>
}


regards, jr.

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This one looks like sliced pita bread or hot dogs buns or something.

#declare Pattern3 = function {tan (3*x) * sin (5*x/2) * sin (z) - 0.1}

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Attachments:
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Preview of image 'mathpatterns2.png'

An interesting approach that I'll have to look into further.

https://gcboore.com/pages/trigonometric-functions.html

Might be able to do the same thing with pigment patterns and homebrew function
patterns.

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On 28/08/2024 22:06, Bald Eagle wrote:
> An interesting approach that I'll have to look into further.
> 
> https://gcboore.com/pages/trigonometric-functions.html
> 
> Might be able to do the same thing with pigment patterns and homebrew function
> patterns.
> 

Really interesting, looking forward to the results of your experiments !
--
YB

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"jr" <cre### [at] gmailcom> wrote:
> "Bald Eagle" <cre### [at] netscapenet> wrote:
> > ...
> > #declare S2P = function (V) {sin (tau*V/L)}
> > #declare C2P = function (V) {cos (tau*V/L)}
> > #declare T = 0.5;
> > #declare N = 1;
> > #declare Honeycomb = function (X, Y, Z) {pow(S2P(X)*C2P(Z) + S2P(Z) + C2P(X), N)
> > - pow(T, N)}
>
> plane with "Honeycomb" pattern, seen through "kaleidoscope".

a loop-able animation of the pattern.  warning -- weird ;-).

<https://drive.google.com/file/d/1Aet9noapf8SBgX2u62TTYMFYx5NfbckT/view?usp=sharing>

enjoy, jr.

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Finally had a moment of clarity, and figured out a fish-scale pattern that I
wanted to make.

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Attachments:
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"Bald Eagle" <cre### [at] netscapenet> wrote:
> Finally had a moment of clarity, and figured out a fish-scale pattern that I
> wanted to make.

And here's a modification to make it less semi-circular.

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