Fashionable Hopefuls: Illustrated Trigonometry with a Side of Turbulence



May 15th, 2020 by Diana Coman

Since this is anyway the second article for today and one coming after going out into the space, no less, let us start with the side for once - aka the turbulence: this is yet another use of the perlin noise, in principle more specifically geared towards gases and other potential sky-textures. The naked effect tends to be quite strong - see the first two images below that adjust the considered pixel size (aka indirectly the number of iterations that apply the noise). Nevertheless, it can perhaps qualify as a different type than previous sets of textures, though to my eye it does tend in any case towards the effect obtained otherwise with several iterations of a multifractal. Comparing it with some of the original pictures and descriptions of this turbulence use that supposedly provides images of perfect-gas (to the extent of even perfect-steam!), I tend to think it takes quite the futzing and the precise fitting to some exact colour scheme to get it to really look like gas/steam. In any case, I could tame down the colours using my own colour mappings that are basically biased towards white (3rd image) and blue (4th image), respectively:

tex_81_512.jpg
tex_82_512.jpg
tex_83_512.jpg
tex_84_512.jpg

The above side aside, the fun part for me was playing with the trig functions as distorters of the domain essentially. And I do wonder now just why on Earth don't they illustrate the 4 quadrants better in all those Maths books, not like it's not possible, have a look (in order, below, the images are obtained with the original colouring scheme, the same scheme only all colours lighetened up a bit; the rgb unit sphere colouring scheme):

tex_51_512.jpg
tex_52_512.jpg
tex_53_512.jpg

The above obviously pack the sin,cos and tan, all in one so it's clear that one *can* separate them too, if so desired - though at the cost of losing that cool reflection-effect, heh. Nevertheless, separating the circle part creates basically a vortex that can further get pastel colours this time by use of worley noise instead of perlin noise (ha, did you think the rgb sphere was always good or the only option for pastel colours? nope, it's not):

tex_55_512.jpg
tex_56_512.jpg

Separating instead the vertical and horizontal threads gets the very illustration of weaving:

tex_54_512.jpg

And since we are weaving cloth of sorts and trying it all out, why not make it a rectangular proper patch and get some truly regular patterns on it, too:

tex_60_512.jpg
tex_61_512.jpg
tex_62_512.jpg
tex_63_512.jpg
tex_64_512.jpg
tex_65_512.jpg

Messing about with the initial domain mapping means that one can turn inside out the four quadrants, of course:

tex_57_512.jpg

Finally, for all the nostalgy of sine waves, here's some quite plain and bold sinus let loose:

tex_58_512.jpg
tex_59_512.jpg

Using two of those turbulence textures as sky this time, the fashion parade wore trigonometry proudly on its skins (and bones):

skel_99_vol7_7_srf7_7_sym_2_tex51_rotxyz52_150_275_640.jpg
skel_99_vol7_7_srf7_7_sym_2_tex52_rotxyz187_187_151_640.jpg
skel_99_vol7_7_srf7_7_sym_2_tex53_rotxyz263_17_346_640.jpg
skel_99_vol7_7_srf7_7_sym_2_tex54_rotxyz180_191_41_640.jpg
skel_99_vol7_7_srf7_7_sym_2_tex55_rotxyz304_341_10_640.jpg
skel_99_vol7_7_srf7_7_sym_2_tex56_rotxyz292_183_239_640.jpg
skel_99_vol7_7_srf7_7_sym_2_tex57_rotxyz14_348_43_640.jpg
skel_99_vol7_7_srf7_7_sym_2_tex58_rotxyz312_223_238_640.jpg
skel_99_vol7_7_srf7_7_sym_2_tex59_rotxyz336_1_267_640.jpg
skel_99_vol7_7_srf7_7_sym_2_tex60_rotxyz28_58_86_640.jpg
skel_99_vol7_7_srf7_7_sym_2_tex61_rotxyz201_97_50_640.jpg
skel_99_vol7_7_srf7_7_sym_2_tex62_rotxyz44_238_216_640.jpg
skel_99_vol7_7_srf7_7_sym_2_tex63_rotxyz324_69_240_640.jpg
skel_99_vol7_7_srf7_7_sym_2_tex64_rotxyz290_4_278_640.jpg
skel_99_vol7_7_srf7_7_sym_2_tex65_rotxyz259_92_332_640.jpg
skel_99_vol7_7_srf7_7_sym_2_tex81_rotxyz313_356_255_640.jpg
skel_99_vol7_7_srf7_7_sym_2_tex82_rotxyz98_169_102_640.jpg
skel_99_vol7_7_srf7_7_sym_2_tex83_rotxyz289_183_181_640.jpg
skel_99_vol7_7_srf7_7_sym_2_tex84_rotxyz171_2_244_640.jpg

And with this I am *finally* caught up on the texture sets and it's good too as I'm clearly starting to shut down the word volume, it's like I wrote way too much those past few days or something. Anyways, having now all of this in the open should help with getting out that explanation re shapes as well so there's that at least still pending.

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8 Responses to “Fashionable Hopefuls: Illustrated Trigonometry with a Side of Turbulence”

  1. Diana Coman says:

    Update: in total contradiction to the very last paragraph of this poor article, my attempt to answer pending questions ended up first of all in... yet another set of textures that I really want at least discussed. So I'll clearly have to write that first and all this - despite my best intentions to stay away from textures at least until the rest of pending stuff is done!

  2. tex_82_512.jpg, tex_82_512.jpg, tex_60_512.jpg, tex_61_512.jpg, tex_62_512.jpg, tex_63_512.jpg, tex_65_512.jpg, should go on the list for the hopeful gen5 dressings. tex_51_512.jpg is indeed the ideal cover for a highschool trig manual ; that it's never been used is just testament to how useless people are, by and large. How did they manage to pass on putting the problem on page 65 or thereabouts, "write the functionals defining the textbook cover illustration" is anyone's guess.

  3. Diana Coman says:

    Got the list and I'll add them. The 82 is repeated in the list - pointing it out just it case it was a 82 and a different one.

    The tex_60_512.jpg looks to me surprisingly well in use - it reminds me of those patterns on some butterflies (Monarch, possibly).

  4. I think I accidentallied it twice, wasn't another one. And yeah, I think the grid thingy may well end up explored further downstream, it's surprisingly natural-looking for how dry it actually is.

    It's also remarkable, in the end, just how anti-Neuman this whole thing is. "Make it look like it was done" heh.

  5. [...] I left the generator code alone for a few days and did instead all the writing of textures and then some more writing and different code and new textures and even various other code tidy ups [...]

  6. [...] made by now a full graphics generator that produces everything, from textures to meshes and full animations too1, I can also finally get out of the existing swamp of data [...]

  7. [...] and complex polynomials on top of everything else, I itch of course to give it a spin with the old style textures too. The only trouble is that such spin is not yet quite available: there's a bit more to implement [...]

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