#mathematicalequations

Being

• Model: Flux Klein

• Size: 3808 X 2176 (8.29 MP)

• Used settings:

  • Prompt: ""Being = Space × Action: Searches for Freedom of Mind Through Mathematics, Art, and Mysticism"; surreal abstract mixed media illustration with scribbled overlays of mathematical formulas, style of Peter Gric, Shaun Tan, and Jaume Plensa's patterns, background of aged cracked parchment with overlays of weathered gold leaf and oxidized patina, ultra detailed, mist, fragmented, grunge background, luminism, colourful, fantastic view, mythical, crisp quality -- ar 1:1
  • Using base image: No
  • Aspect Ratio: landscape_wide

Futuristic Laboratory of Floating Equations

• Model: Grok

• Size: 3200 X 2400 (7.68 MP)

• Used settings:

  • Prompt: $$\boldsymbol{\Sigma}_{\sim} = \oint_{\Gamma} \left[ e^{i \sin(\omega \tau \cdot \mathcal{L}_\chi)} \star\left( \nabla^\mu \partial_\mu \mathbf{T}\mathcal{O}^\nu \otimes \partial^\rho \mathbf{T}^*\mathcal{C}^\sigma \right) \otimes e^{-i \sin(\omega \tau \cdot \mathcal{L}_\chi)} \star\left( \partial^\rho \mathbf{T}^*\mathcal{C}^\sigma \otimes \nabla^\mu \mathbf{T}\mathcal{O}^\nu \right) \right] \wedge \star (d\tau \wedge d\Omega_{\phi})$$
  • Using base image: No
  • Aspect Ratio: landscape

Confident Smile in a Bright Classroom

• Model: Z-Image Turbo

• Size: 1280 X 960 (1.23 MP)

• Used settings:

  • Prompt: A realistic, high-definition photo of a Very beautiful and attractive Indian woman, with slender body, full body view, cute smile, wearing a vibrant dual-shaded georgette saree. The saree features a seamless ombre gradient transitioning from bright lemon yellow at the top to a warm sunset orange at the bottom. The fabric is lightweight, semi-transparent, and drapes elegantly with soft, fluid folds. She is wearing a simple white sleeveless blouse. The background is a brightly lit, slightly blurred classroom setting with a green chalkboard filled with white mathematical equations. She has both arms raised behind her head, elbows pointing outward, with her fingers tucked into her hair as if adjusting a ponytail. Her posture is confident and upright, facing the camera directly.
  • Using base image: No
  • Aspect Ratio: landscape

Celestial Ascendance: A Cosmic Vision

• Model: Nano Banana 2 (Pro)

• Size: 1200 X 896 (1.08 MP)

• Used settings:

  • Prompt: A human figure suspended in midair, their body dissolving into swirling fractals of golden light that merge seamlessly with the surrounding cosmos. Reality warps around them—geometric patterns of cities, forests, and galaxies unfold and collapse like origami within their translucent form. Their face is serene, eyes glowing with infinite depth as strands of luminous data cascade through their outstretched hands. The background is a void of deep indigo, pulsing with ephemeral neon equations that shift like living code. A sense of transcendent unity radiates from the scene, where boundaries between flesh, thought, and universe blur into pure awareness.
  • Using base image: No
  • Aspect Ratio: landscape

Travel diary from Toulouse 1

• Model: Nano Banana 2

• Size: 2480 X 3312 (8.21 MP)

• Used settings:

  • Prompt: Expressive watercolor portrait illustration blended with mixed-media collage, semi-realistic painterly style, soft yet dramatic brush strokes, layered translucent watercolor washes, visible paper texture, organic paint blooms and splatters, muted earthy color palette (warm browns, sepia, dusty blues, soft grays), subtle ink outlines, abstract facial planes, gentle color bleeding, editorial illustration aesthetic, intellectual and contemplative mood, minimal background with faded vintage newspaper text, handwritten notes, mathematical formulas and diagram overlays, textured off-white paper backdrop, fine art illustration, modern–classic fusion, high artistic depth, calm cinematic lighting, elegant and thoughtful atmosphere."
  • Using base image: Yes

Platonic * Love

• Model: FluX 2 (Ultra)

• Size: 2880 X 2880 (8.29 MP)

• Used settings:

  • Prompt: The image is a double exposure of a Bumble Bee flying into the space of Holgerion*s Universe. The background contains some mathematical equations and graphs in the mysterious world of the jewish Kabbala . The image has a rough texture and is hyper-detailed with a muted palette of teak brown, crimson, gold, deep blue, and indigo black. There are some sharp lines, dripping waterpaint and ink, and a glowing and sparkling effect in delicate colours ! Make it in Multilayer Rendering and Highest Resolution !
  • Using base image: Yes

Cosmic Journey of a Running Dreamer

• Model: FluX 2 (Ultra)

• Size: 2880 X 2880 (8.29 MP)

• Used settings:

  • Prompt: dark ethereal surreal horror art, dark surrealism with elements of glitch-art, datamoshing and pixel-sorting, hyperdetailed, 8K resolution, alcohol ink, maximalist, extremely detailed, high contrast, paint and ink, elegant being ran down before drying, glowing and sparkling, rough texture, complete universe texture as close-up within a planetary nebula with ethereal gas clouds, stars and the fantastic structures of celestial wonder. cracked texture. small damage to the image, like cracks and torn off surface with black inside, soft edges. everything in the colors of nebula contrasted against the dark background of space. a female featureless face wearing a tattered hood, empty starstruck eye-sockets, within her a double exposure displaying the infinite universe as ethereal, atmospheric. planetary nebula with ethereal gas clouds, stars and the fantastic structures of celestial wonder. the face and hood partially dissolved into nebular gas clouds, the eyes like gas clouds and stars. in a photorealistic way, reminiscent of astronomic imagery. a small diffuse, glitchy, skirt-clad female silhouette, facing away, walking an ethereal trail into the infinite, below the face while retaining the contrast and dark theme. scientific handwriting such as equations and scientific text notes as part of the overall texture. Beautiful and awe-inspiring. Extremely high quality, masterpiece, excellent.
  • Using base image: No
  • Aspect Ratio: square

Govern the country according to my formula and you won't need war.

• Model: Grok

• Size: 3783 X 2128 (8.05 MP)

• Used settings:

  • Prompt: In a dreamlike, avant-garde classroom, a teacher with dark, expressive features and disheveled hair wears a tailored dark maroon double-breasted jacket. He is captured mid-lecture, hands gesturing wildly toward a massive canvas blackboard covered in a chaotic, beautiful mess of golden calculus equations and magenta graffiti. The style is a fusion of street art and fine art portraiture, reminiscent of Tim Gill's textured, layered aesthetic. The background is a wash of pastel violet and shocking pink ink stains. The teacher's face is partially obscured by shadows, creating a mystic, scholarly aura. Mathematical symbols float slightly off the surface of the wall, interacting with sketched heraldic symbols. Cinematic lighting, soft bokeh, and rich color grading.
  • Using base image: No
  • Aspect Ratio: landscape_wide

Galactic Equations: A Cosmic Exploration

• Model: Grok

• Size: 2532 X 1424 (3.61 MP)

• Used settings:

  • Prompt: Ultra-sharp 8K scientific illustration of a glowing black-hole spacetime with the following complete non-standard Schwarzschild metrics: 1. Grok conceptual I ds² = −(1 − r_s/arcsinh(r'))c² (dt'²/(d ln(1+t/t_s)/dt')² + (1 − r_s/arcsinh(r'))⁻¹(dr'/d arcsinh(r))² dr² + (r'/arcsinh(r))² d(tan θ')² + (r'/arcsinh(r))² sin(tan θ'))² dφ² where r' = arcsinh(r), θ' = tan(θ), t' = ln(1 + t/t₀) 2. Grok conceptual II (latest mutation) ds² = −(1 − r_s/arcsinh(tan r))c²/(t₀ + t)² dt² + (1 − r_s/arcsinh(tan r))⁻¹ sec⁴ r dr² + (tan r/sinh r)² cosh² θ dθ² + (tan r/sinh r sin(sinh θ))² dφ² 3. ChatGPT hyperbolic form ds² = −(1 − 2GM/sinh x)c² dT²/T² + (1 − 2GM/sinh x)⁻¹ cosh² x dx² + sinh² x [du²/(1+u²)² + u²/(1+u²) dφ²] 4. Ricci-flat axis-separable hybrid ds²ᵖⁱ = −ln(sinh(t + ε sin(ωt))) dt²ᵖⁱ + tan⁻ᵖⁱ(x + ε cos(kx)) dx²ᵖⁱ + cosh(y + ε sinh(ωy)) dy²ᵖⁱ + sinh(z + ε cos(kz)) dz²ᵖⁱ (ε=0.001275, ω=1.618, k=16.78544587)
  • Using base image: No
  • Aspect Ratio: landscape_wide

...

• Model: Kling 3

• Size: 2160 X 3824 (8.26 MP)

• Used settings:

  • Prompt: Cliff Diver into Fractal Water—mid-air silhouette suspended above an ocean of shifting geometric patterns, where each splash spirals into infinite shapes, turning the plunge into a dive through living mathematics.
  • Using base image: No
  • Aspect Ratio: portrait_tall

Whimsical Exhale of Thought

• Model: SeeDream

• Size: 1568 X 2368 (3.71 MP)

• Used settings:

  • Prompt: In the world of Fragile Vision, every painting begins not with colour, but with a breath, a quiet fragment of poetry. From that breath, pigment drifts outward, carrying emotions too delicate for speech. Full brilliantly coloured red, green, blue, brown. Artist Jean-Baptiste Monge style. The pale ultra-pale hyper-pale half body portrait, cute Kyoto girl, traditional short mini skirt, in dynamic pose, a print of mathematical equations, astrological signs, glossy spheres of symbols, against a backdrop of drippy fungi mycelium slime mold, splash paint over robes, hieroglyphics symbols, alien calligraphy with Gestural Flourishes, ripples, Skips, Feathering, bleeding from indian ink, sketches of graph & waves, impasto oil painting, dark, abstract, ominous, style of Dave McKean and Stephen Gammell.
  • Using base image: Yes

Cruise Ship Journey to Silver Harbor

• Model: Grok

• Size: 2560 X 1472 (3.77 MP)

• Used settings:

  • Prompt: A A huge cruiser in the silver harbor, intricately crafted with mathematical formulas against the background of mathematics. The artwork is a masterpiece with double exposure, vibrant colors, and exquisite detail, radiating a majestic and legendary aura., extremely detailed, a masterpiece, clearly worked out details, Double exposure, highly detailed, elegant Fantastic, exciting, majestic, legendary, epic, colorful, sublime, gentle radiance, high detail elaboration, Sunshine rays, super crisp quality, super unreal, ultra-clear image, ultra-confusing, ultra-high definition, ultra-pronounced detail
  • Using base image: Yes

Cosmic Whale in a Nebula Dreamscape

• Model: AI Upscaler

• Size: 3520 X 2352 (8.28 MP)

• Used settings:

  • Prompt:
  • Using base image: Yes

Artistic Exploration of Freedom and Identity

• Model: SeeDream

• Size: 2224 X 1664 (3.70 MP)

• Used settings:

  • Prompt: ""Being = Space × Action: Searches for Freedom of Mind Through Art, and Mysticism"; surreal abstract mixed media illustration with scribbled overlays of mathematical formulas, style of Peter Gric, Shaun Tan, and Jaume Plensa's patterns, background of aged cracked parchment with overlays of weathered gold leaf and oxidized patina, ultra detailed, mist, fragmented, grunge background, luminism, colourful, fantastic view, mythical, crisp quality, by Susanne
  • Using base image: No
  • Aspect Ratio: landscape

Exploring the Mysteries of the Vortex Tunnel

• Model: (Mode 20)

• Size: 1024 X 1024 (1.05 MP)

• Used settings:

  • Prompt: The funnel entangles the astronomer. The image presents a contemplative yet unsettling scene in which an astronomer is caught within the widening spiral of a massive funnel, not physically trapped but conceptually absorbed. The funnel narrows and expands simultaneously, suggesting competing forces of focus and confusion. The astronomer’s instruments—charts, lenses, and notebooks—hover nearby, partially drawn inward, as if the pursuit of cosmic knowledge itself has become a constricting mechanism. The astronomer’s expression is intent rather than fearful, conveying fascination, surrender, and intellectual vulnerability. The entanglement feels cerebral, as though curiosity has crossed into obsession. The entire environment is infused with mercury, which pools across the ground and rises into the background. Its reflective surface mirrors distorted stars, diagrams, and fragments of the astronomer’s form, creating shimmering doubles that destabilize orientation. Ripples in the mercury suggest motion without wind, reinforcing a sense of quiet unease and fluid logic. Rendered in a Leonardo da Vinci drawing style, the image emphasizes precise line work, anatomical study, and observational rigor. Soft sepia tones, cross-hatching, and delicate shading lend the scene a Renaissance quality, blending scientific inquiry with philosophical introspection.
  • Using base image: No
  • Aspect Ratio: square

Vibrant Patterns and Mathematical Harmony

• Model:

• Size: 1536 X 1536 (2.36 MP)

• Used settings:

  • Prompt: \newcommand{\bea}{\begin{eqnarray}} \newcommand{\eea}{\end{eqnarray}} \bea\label{V1} G_{00}+G_{11}=(\alpha^2+\beta^2)g_{MN}\frac{d\tilde{X}^M}{d\xi}\frac{d\tilde{X}^N}{d\xi} +2\beta\Lambda^\mu g_{\mu N} \frac{d\tilde{X}^N}{d\xi} +\Lambda^\mu\Lambda^\nu g_{\mu \nu} =0,\eea \bea\label{V2} G_{01}&=&\alpha\beta g_{MN}\frac{d\tilde{X}^M}{d\xi}\frac{d\tilde{X}^N}{d\xi}+\alpha\Lambda^\mu g_{\mu N}\frac{d\tilde{X}^N}{d\xi} =0,\eea \bea\nn &&-(\alpha^2-\beta^2)\left[g_{LK}\frac{d^2\tilde{X}^K}{d\xi^2}+ \Gamma_{L,MN}\frac{d\tilde{X}^M}{d\xi}\frac{d\tilde{X}^N}{d\xi}\right] +2\beta\Lambda^\mu\Gamma_{L,\mu N}\frac{d\tilde{X}^N}{d\xi} +\Lambda^\mu\Lambda^\nu \Gamma_{L,\mu\nu} \\ \label{EM} &&= \alpha\Lambda^\mu H_{L\mu N}\frac{d\tilde{X}^N}{d\xi},\eea \bea\label{Q} &&Q_{\mu}= \frac{T}{\alpha}\int d\xi\left[\left(\beta g_{\mu N}+\alpha b_{\mu N}\right)\frac{d\tilde{X}^N}{d\xi}+\Lambda^\nu g_{\mu \nu}\right].\eea
  • Using base image: No
  • Aspect Ratio: square

If the world is not logical, it cannot be understood with logic

• Model:

• Size: 2688 X 1512 (4.06 MP)

• Used settings:

  • Prompt: Theme: If the world is not logical, it cannot be understood with logic. A solitary figure stands on a floating, broken stone fragment above a soft, rippling sea of ink and color. The world around slowly dissolves into painterly strokes, as if reality is melting into a dream. Mathematical formulas drift through the air — not sharp, but hand-drawn, imperfect, half-finished: integrals, spirals, fractured numbers, unfinished equations. They slowly unravel into abstract lines, soft smoke, and flowing color. Below, the water does not reflect reality clearly — instead it shows a distorted, surreal version of the world: waves made of numbers, faces emerging from symbols, eyes made of infinity signs, trees growing from spirals. In the sky, the universe is painted like a dream: swirling galaxies, soft nebulae, abstract constellations, floating symbols and gentle geometry that dissolves at the edges — not mathematical perfection, but living, fluid chaos. Some formulas transform into birds mid-air, others become glowing threads that stitch and un-stitch the sky itself. Style influences: – surreal painting – abstract symbolism – dreamy spiritual art – soft painterly brush strokes – slight impressionism + visionary art – inspired by Salvador Dalí, Alex Grey, Android Jones, and cosmic watercolor Color palette: deep indigo, ultramarine, antique gold, soft lavender, warm ivory, hints of turquoise and crimson Lighting: soft, ethereal glow, no hard realism, painterly light Mood: mystical — calm — wise — slightly cryptic — beautiful
  • Using base image: No
  • Aspect Ratio: landscape_wide

Vortex of Mathematics and Physics Unveiled

• Model:

• Size: 1536 X 1536 (2.36 MP)

• Used settings:

  • Prompt: \begin{align} \label{spin2descendant} P_i\p{z^{-\Delta}K_i\otimes K_j}&=\p{P_iz^{-\Delta}}K_i\otimes K_j+z^{-\Delta}[P_i,K_i]\otimes K_j+z^{-\Delta}K_i\otimes [P_i,K_j] \notag\\ &=2 z^{-\Delta} \p{-\Delta r_i K_i\otimes K_j-d D\otimes K_j+K_i\otimes iJ_{ji}-K_j\otimes D } \notag \\ P_i\p{z^{-\Delta}K_j\otimes K_i}&=\p{P_iz^{-\Delta}}K_j\otimes K_i+z^{-\Delta}[P_i,K_j]\otimes K_i+z^{-\Delta}K_j\otimes [P_i,K_i] \notag \\ &=2z^{-\Delta}\p{-\Delta K_j\otimes r_iK_i-dK_j\otimes D+iJ_{ji}\otimes K_i-D\otimes K_j} \notag \\ \frac{2}{d}P_j\p{z^{-\Delta}K_m\otimes K_m}&= 2z^{-\Delta}\p{-\frac{2\Delta}{d}r_j K_m\otimes K_m+ \frac{2}{d}\p{iJ_{mj}\otimes K_m+K_m\otimes iJ_{mj}}-\frac{2}{d}\p{D\otimes K_j+K_j\otimes D}} \end{align} In order to satisfy the null state condition, such a state has to be a primary state which is annihilated by $K_\ell$, which gives: \begin{align*} K_\ell\left[P_i\p{\mathcal{O}_{ij}}\right]=z^{-\Delta}\p{(\Delta-d-2)\p{K_j \otimes K_\ell+K_\ell \otimes K_j}+\p{2-\frac{2\Delta}{d}+\frac{4}{d}}\delta_{j\ell}K_m\otimes K_m} \end{align*} We see that this will vanish only if $\Delta=d+2$. Using the coordinates (\ref{newcoordinate}), and expressing the rotational generator in terms of the special conformal transformation, we can express (\ref{spin2descendant}) with $\Delta=d+2$ more compactly as: \begin{align} P_i\p{\mathcal{O}_{ij}}=-\frac{(d+2)(d-1)}{d\cdot z^{\Delta}}\p{\tilde \Delta\otimes K_j+K_j\otimes \tilde \Delta} \end{align} where we have $\tilde{\Delta}=D+r^iK^i$
  • Using base image: No
  • Aspect Ratio: square

Empowering Education Through Mathematics

• Model: DaVinci2

• Size: 1016 X 1016 (1.03 MP)

• Used settings:

  • Prompt: The teacher [women] is standing at the blackboard, beautiful mathematical formulas are written on the board.
  • Using base image: Yes

Vibrant Swirls of Mathematical Artistry

• Model:

• Size: 1024 X 1024 (1.05 MP)

• Used settings:

  • Prompt: Draw and render a: Shape: ds^{24.123321\pi} = \frac{ -dt^{12.8778\pi} + dr^{16.7887\pi} + \sin^{14.45877854\pi}\cdot\text{r} \, d\Omega^\{12.278\pi}}{4 \cos^{12.44\pi}\cdot\text{t} + r^{2\pi} \cos^{2\pi}\cdot\text{t} - r^{2.5665\pi}} Iteration count = 512 Textured by: t = \frac{1}{2\pi}\left[\tan\left(\frac{\bar{t}+\hat{r}}{2}\right) + \tan\left(\frac{\bar{t}-\hat{r}}{2}\right)\right], \quad r = \frac{1}{2\pi}\!\left[\tan\!\left(\frac{\bar{t}+\hat{r}}{2}\right) - \tan\left(\frac{\bar{t}-\hat{r}}{2}\right)\right].
  • Using base image: No
  • Aspect Ratio: square