#torus

Iridescent Torus in a Sea of Equations

• Model: AIVision (Ultra)

• Size: 2560 X 1472 (3.77 MP)

• Used settings:

  • Prompt: Apply tensor product of the {1.6180339887498948482045868343656\pi\sqrt[\exp(1)]{2\cdot1.6180339887498948482045868343656}}-form of the tangent bundle of the orbifold over the {1.6180339887498948482045868343656\exp(1)\sqrt[\pi]{2\cdot1.6180339887498948482045868343656}}-form of the tangent bundle of the conifold !
  • Using base image: No
  • Aspect Ratio: landscape_wide

Geometric Torus with Mathematical Elegance

• Model: AIVision

• Size: 1536 X 1536 (2.36 MP)

• Used settings:

  • Prompt: (initialized with:0.00125): t = \frac{1}{2.4774\pi}\left[\tan\left(\frac{\tilde{t}+\tilde{r}}{2}\right) + \tan\left(\frac{\tilde{t}-\tilde{r}}{2}\right)\right], r = \frac{1}{2.4774\pi}\left[\tan\left(\frac{\tilde{t}+\tilde{r}}{2}\right) - \tan\left(\frac{\tilde{t}-\tilde{r}}{2}\right)\right] (Iteration count:2048) Draw and render a shape: ds^{48.123321\pi} = \frac{ -dt^{2.8778\pi} + dr^{2.7887\pi} + \sin^{1.445877854\pi}\cdot\text{r} , d\Omega^{1.2278\pi}}{4.785587 \cos^{2.144\pi}\cdot\text{t} + r^{2.7447\pi} \cos^{2.4774\pi}\cdot\text{t} - r^{2.5665\pi}};
  • Using base image: No
  • Aspect Ratio: square

Sleek Black and Purple Textured Torus Design

• Model: DaVinci2

• Size: 1152 X 864 (1.00 MP)

• Used settings:

  • Prompt: A render of an object with power \( P = 11.24788742\pi \), fixed iterations \( \text{LOOPS} = 256 \), initialized as \( z = \text{chp}(p) * p - p \) where \( \text{chp}(x) = \frac{(\exp(x) + \exp(-x))}{\pi} \), \( \text{shp}(x) = \frac{(\exp(x) - \exp(-x))}{\pi} \), \( \text{chpp}(x) = \frac{(\exp(x / (\cosh(x) \pi)) + \exp(-x / (\cosh(x) / \pi)))}{2 \pi \Phi} \), \( \text{shpp}(x) = \frac{(\exp(x \sinh(x) \pi) - \exp(-x \sinh(x) \pi))}{2 \pi \Phi} \), \( \text{ssh1}(x) = \frac{\sinh(x / \pi)}{\Phi} \), \( \text{csh1}(x) = \frac{\cosh(x / \pi)}{\Phi} \), \( \Phi = \frac{(1 + \sqrt{5})}{2} \) golden ratio, \( \tau = 2 \pi * 0.7887 \); iteration: \( r = ||z|| \), if \( r > 2 \) continue, \( \theta = \text{asin}(z_z / r) + 0.2t \) animated, \( \varphi = \text{atan}(z_x, z_y) \), \( dr = r^{P - 1} dr P + 1 \), \( r = r^P \), \( \theta = \theta P / \Phi \), \( \varphi = \varphi P / \Phi \), \( z += r * (\tan(\text{shp}(\sin\theta \sin\varphi)) \Phi, \text{chp}(\cos\theta \sin\varphi), \cos\varphi) + p \), \( p = \text{reflect}(p, z) \), final \( \text{DE} = 0.75 \log(r) r / dr \) scaled by \( \text{shp}(\text{DE} * 2) \); ray-marched with max marches = 96, tol = 10^{-5}, bounces = 8, refraction index 1.01275, Beer absorption \( \exp(-(t + 0.1) * -\text{HSV}(0.05, 0.95, 2)) \), diffuse \( \text{HSV}(0.6, 0.85, 1) \), glow \( \text{HSV}(0.065, 0.8, 6) \), sky \( \text{HSV}(0.6, 0.86, 1) \) with warped reflections via ssh1, chpp, \( \text{fract}(\text{clamp}(0.125 / |\text{reflected cross}| * \text{skyCol}, -120, 16.547)) \); rotated by \( \text{rot\_x}((1.221 t + \pi) / \tau) \), camera at \( (0, 2, 5) * 0.6 \), FOV \( \tan(\tau / 6) \), ACES tone-mapped, sRGB gamma; central bulbous form with pink core, orange lobes, black voids, cyan shell, rainbow tunnel background. Apply: TE \otimes_{TB} TF \xrightarrow{h_E \otimes h_F} TE \otimes_{TB} TF \xrightarrow{\ \ \ \ \tau\ \ \ \ } T(E \otimes F). vec3 col = fract(clamp(vec3(0.125/abs(reflect(cross(rd,ro),reflect(shpp(ro),chpp(rd))).z))*skyCol, -120.0, 16.54788745));
  • Using base image: No
  • Aspect Ratio: landscape

Surreal Geometry in a Dreamlike Landscape

• Model: AIVision

• Size: 2236 X 2236 (5.00 MP)

• Used settings:

  • Prompt: Show a real-world example of Euler's identity. Include a Klein bottle, a mobius strip, or a pseudosphere as part of the image.
  • Using base image: No
  • Aspect Ratio: square

Colorful Torus on Black Surface

• Model:

• Size: 1607 X 1244 (2.00 MP)

• Used settings:

  • Prompt: A perfect depiction of a Klein bottle, drawn in the style of Theodore Roczak, but with oil pastels
  • Using base image: No
  • Aspect Ratio: landscape

Glow

• Model: AIVision

• Size: 1792 X 1024 (1.84 MP)

• Used settings:

  • Prompt: Purple and Pink Crystal Ball filled with a black hole surrounded by mini suns of different sizes and luminance .
  • Using base image: No
  • Aspect Ratio: landscape

Ethereal Galactic Torus

• Model: Artistic

• Size: 896 X 704 (0.63 MP)

• Used settings:

  • Prompt: Doxa fuego bioluminiscente
  • Using base image: No
  • Aspect Ratio: landscape

Iridescent Bubbles on a Green Canvas

• Model: Artistic

• Size: 2831 X 1770 (5.01 MP)

• Used settings:

  • Prompt: One only colorful circle with bubbles. Machine processing Nikon D850 sharp focus Award winning photography fantasy intricate 8k very attractive dynamic lighting imperial colors fantastic view ultra detailed 4K 3D high definition crisp quality colourful Ilya Kuvshinov sensual Nicoletta Ceccoli No hands Vasarely Margaret Keane Laura Diehl Zdzislav Beksinski no deformities fit the subjects within the picture frame.
  • Using base image: Yes

isogeneous

• Model: Artistic

• Size: 896 X 704 (0.63 MP)

• Used settings:

  • Prompt: isogeneous
  • Using base image: No
  • Aspect Ratio: landscape

torus 6.1.9

• Model: Artistic

• Size: 1449 X 1449 (2.10 MP)

• Used settings:

  • Prompt: change nothing
  • Using base image: Yes

torusausage

• Model: Artistic

• Size: 896 X 704 (0.63 MP)

• Used settings:

  • Prompt: torusausage
  • Using base image: No
  • Aspect Ratio: landscape

toroidal sausages

• Model: Artistic

• Size: 896 X 704 (0.63 MP)

• Used settings:

  • Prompt: toroidal sausages
  • Using base image: No
  • Aspect Ratio: landscape