#torus

Sacred Geometry Winterscape

• Model: FluX (Ultra)

• Size: 2560 X 1440 (3.69 MP)

• Used settings:

  • Prompt: Geometric Winter A professional, ultra-high resolution photograph capturing a surreal winter landscape where snow, ice, and light combine to form complex sacred geometry. A vast, frozen lake, its icy surface cracked into precise patterns forming a massive Metatron's Cube covering the foreground. The surrounding landscape is a silent forest of ancient pine trees, their branches laden with hyper-detailed snow that sparkles like microscopic diamonds. A pale silver full moon hangs in the deep midnight blue sky, casting cold, ethereal light. Directly beneath the moon, a monumental, crystalline Torus structure, composed entirely of glowing blue and white light, levitates silently above the lake, its form pulsing softly. Integrated into the snowdrifts are megalithic stones etched with glowing Nordic runes and the alchemical symbol for Water. Millions of tiny, floating geometric ice crystals are suspended in the volumetric moonlight. A lone figure stands at the edge, a lantern etched with the Eye of Providence in hand. The palette is monochromatic and sophisticated.
  • Using base image: No
  • Aspect Ratio: landscape_wide

Iridescent Torus: A 3D Abstract Journey

• Model: FluX 2 (Pro)

• Size: 2224 X 1664 (3.70 MP)

• Used settings:

  • Prompt: TORE PLAT FRACTALE LISSE CORRUGATIONS
  • Using base image: No
  • Aspect Ratio: landscape

Iridescent Torus in a Sea of Equations

• Model: (Mode 30)

• 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:

• 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:

• 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:

• 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

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