#mathematicalequations

Exploring the Mysteries of the Vortex Tunnel

• Model: (Mode 20)

• Size: 1024 X 1024 (1.05 MP)

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  • 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

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• Size: 1536 X 1536 (2.36 MP)

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  • 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

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• Size: 2688 X 1512 (4.06 MP)

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  • 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

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• Size: 1536 X 1536 (2.36 MP)

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  • 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 $\tilde{\Delta}=D+r^iK^i$
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  • Aspect Ratio: square

Empowering Education Through Mathematics

• Model: DaVinci2

• Size: 1016 X 1016 (1.03 MP)

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  • 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

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• Size: 1024 X 1024 (1.05 MP)

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  • 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].
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  • Aspect Ratio: square

Abstract Sphere of Scientific Exploration

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• Size: 1536 X 1536 (2.36 MP)

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  • Prompt: Generate the following: Represent 3D points in spherical coordinates where \( r = \sqrt{x^{2\pi} + y^{2\pi} + z^{2\pi}} \), \( \theta = \text{acos}(z/r) \), \( \phi = \text{atan2}(y, x) \). The power operation \( v^n = r^n \cdot [\sin(n\theta) \cos(n\phi), \sin(n\theta) \sin(n\phi), \cos(n\theta)] \). Iteration: \( v_{k+1} = v_k^n + c \), starting from \( v_0 = (0,0,0) \), with escape if \( |v_k| > 24.78 \) after 64 iterations. Use ray marching with distance estimator \( DE(p) \approx (1/2) \cdot (r - R) / |dr/dv| \) for rendering, applying escape-time coloring, orbit traps, and Phong shading for neon glow effects. Using also: $$ \sum_{n=0}^\infty \left(\frac{1}{2^n}\right), \quad \int_{-\infty}^\infty e^{-x^2} \, dx = \sqrt{\pi}, \quad f(x) = x^2 + c, \quad z_{k+1} = z_k^2 + c, \quad |z| = \sqrt{x^2 + y^2}, \quad z = r e^{i\theta}, \quad z^2 = r^2 e^{i2\theta}, \quad x' = r^2 \cos(2\theta), \quad y' = r^2 \sin(2\theta) $$ $$ r = \sqrt{x^{2\pi} + y^{2\pi} + z^{2\pi}}, \quad \theta = \text{acos}(z/r), \quad \phi = \text{atan2}(y,x), \quad v^n = r^n [\sin(n\theta)\cos(n\phi), \sin(n\theta)\sin(n\phi), \cos(n\theta)], \quad v_{k+1} = v_k^n + c, \quad DE \approx \frac{1}{2}\frac{(r-R)}{|dr/dv|} $$ along with additional generic math like \( \sum \), \( \int \), \( \frac{\partial}{\partial x} \), \( \lim_{x\to\infty} \), \( \Gamma(z) \), \( \zeta(s) \), and graphs of functions such as sine waves, parabolas, and axes arrows. Ensure the composition is centered on the fractal with soft glows, high resolution, surreal and mathematical aesthetic, similar to AI-generated fractal art in a cosmic math universe.
  • Using base image: No
  • Aspect Ratio: square

Art Meets Science in Vibrant Abstract Sketch

• Model: FluX

• Size: 864 X 1152 (1.00 MP)

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  • Prompt: PUSSYART, WHISKAS CONTOUR, , DRAWING, minimalist abstract depiction of a figure with abstract body contour. Iridescent multicolor, sheen, glow, abstract brushstrokes. Elegant flowing form with gentle curves and subtle contours from head to hips, balanced and harmonious. Zen lines, serene and luminous, SCRIBBLED on a page with written MATHEMATIC CALCULATIONS
  • Using base image: No
  • Aspect Ratio: portrait

Looking * for * Gravity

• Model: FluX

• Size: 1296 X 1728 (2.24 MP)

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  • Prompt: The image is a double exposure of a Bumble Bee flying into the cosmic space. The background contains mathematical equations and graphs. The image has a rough texture and is hyper-detailed with a muted palette of brown, crimson, gold, blue, and black. There are sharp lines, dripping paint and ink, and a glowing and sparkling effect for a surreal intergalactic feeling Multilayer Rendering Highest Resolution Mode
  • Using base image: No
  • Aspect Ratio: portrait

Thoughtful Young Woman

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• Size: 1832 X 1368 (2.51 MP)

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  • Prompt: Being = Space × Action: Searches for Freedom of Mind Through Mathematics, Art, and Mysticism"; a surreal, colourful masterpiece with scribbled overlays of mathematical formulas, 3/4 side portrait of a woman, deep iridescent vibrant colors, luminism, dreamy atmosphere; by Susanne, 4K3D.
  • Using base image: No
  • Aspect Ratio: landscape

Whimsical Scholar in a Mathematical World

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• Size: 1024 X 1024 (1.05 MP)

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  • Prompt: miniature size in the corner of the page, woman sketch in love student excercise book scribble, surrounded by numbers, calculations, equations and curves, mathematician drawing different curves on graph paper, from curves comes the (simplisized outer silhouette of slim metart) (empty inside) , , (stop) , best view, torment, self enjoyment rubbing, bralette and hip skirt, (promiscuous, kinky, vulgar),
  • Using base image: No
  • Aspect Ratio: square

Anatomy of Time

• Model: AI Upscaler

• Size: 5545 X 3025 (16.77 MP)

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  • Using base image: Yes

The Quantum Geometry of Time

• Model: AI Upscaler

• Size: 5549 X 3021 (16.76 MP)

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  • Prompt:
  • Using base image: Yes

Surreal Chess Game of Elegantly Dressed Figures

• Model: FluX

• Size: 1024 X 1024 (1.05 MP)

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  • Prompt: Cubism, magic realism This tableau evokes a surreal juxtaposition: academic rigor encoded in chalk glyphs—equations and chessboards—intertwined with aesthetic contradiction and theatrical flair. The three figures, dressed in intimate formalwear and fishnet stockings, stand as a triad: lecturers of paradox, perhaps symbols of Banksian dialectics in corporeal form. This scene may depict the ceremonial First Recursion of Gödel’s Glamour, wherein the Academy initiates a new paradox lens. Students are challenged to resolve logic without stripping away aesthetics. One must understand why this is both satire and ritual. And why the board is not set for play—but for recursion.
  • Using base image: No
  • Aspect Ratio: square

Ethereal Glitch Art: A Surreal Journey

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• Size: 1920 X 1080 (2.07 MP)

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  • Prompt: (((glitch art masterpiece, datamoshing, pixelation, bent image, randomness))) dark ethereal surreal horror art, dark surrealism, hyperdetailed, 8K, airbrush art, ink drawing, alcohol ink, vibrant palette of blue, silver and black, maximalist, extremely detailed, high contrast, sharp lines, dripping paint and ink, elegant, glowing and sparkling, rough texture, female figure, no-face, empty eye-sockets, double exposure, a person walking a trail into the infinite, mathematical equations, ...
  • Using base image: No
  • Aspect Ratio: landscape_wide

Ethereal Glitch: A Journey into Darkness

• Model: FluX

• Size: 1920 X 1080 (2.07 MP)

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  • Prompt: (((glitch art masterpiece, datamoshing, pixelation, bent image, randomness))) dark ethereal surreal horror art, dark surrealism, hyperdetailed, 8K, airbrush art, ink drawing, alcohol ink, vibrant palette of blue, silver and black, maximalist, extremely detailed, high contrast, sharp lines, dripping paint and ink, elegant, glowing and sparkling, rough texture, female figure, no-face, empty eye-sockets, double exposure, a person walking a trail into the infinite, mathematical equations, ...
  • Using base image: No
  • Aspect Ratio: landscape_wide

Galactic Wisdom: Merging Science and Spirit

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• Size: 4096 X 4096 (16.78 MP)

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  • Prompt: Create a glitch art masterpiece inspired by datamoshing, pixelation, and bent image elements. The image consists of a dark, ethereal, and surrealist style reminiscent of cubism. It is extremely detailed, presented with a muted palette of brown, crimson, gold, blue, and black, and painted in 8K resolution. The medium is airbrush art, similar to an ink drawing or alcohol ink, with visible drips of paint and ink. It entails maximalist aesthetics with high contrast, sharp lines, a subtle glow, sparkles and a rough texture, adding drama to this elegant piece. Central to this image is a detailed rendering of a female figure, her descent undisclosed. Her facial elements are cloaked, and in place of her eyes are empty sockets. The cloak is double-exposed with an image of the Universe, while mathematical equations and stars are seen within the hood. A well-rendered DNA helix forms a frame around her. The figure seems to be an allegory of our connection to the stars and the mystery of existence.
  • Using base image: No
  • Aspect Ratio: square

Cosmic Silhouette: Art Meets Science

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• Size: 4096 X 4096 (16.78 MP)

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  • Prompt: (((glitch art masterpiece, datamoshing, pixelation, bent image, randomness))) dark ethereal surreal horror art, dark surrealism, cubism, hyperdetailed, 8K, airbrush art, ink drawing, alcohol ink, vibrant palette of crimson+gold+black, maximalist, extremely detailed, high contrast, sharp lines, elegant, glowing and sparkling, rough texture, female figure, no-face, empty eye-sockets, profile view, mathematical equations, stars
  • Using base image: No
  • Aspect Ratio: square

mathematical equations

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• Size: 1536 X 1536 (2.36 MP)

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  • Prompt: Ethereal religious icon, alabaster skin with cracks, amber-green almond eyes, somber expression, tattered hood, aged plaster background, nature elements in cracks, delicate leaves and twigs, sacred and natural merge, Agostino Arrivabene, Sam Wolfe Connelly, Sverre Malling, Karla Ortiz, Kiki Smith, Lotta Blokker, Pamela Wilson, Heidi Taillefer, GoBi design, mystical, haunting, contemplative, detailed, high cheekbones, wisdom and sorrow, reverence, ethereal, cracked skin texture, deep emotion, intelligent gaze, timeless, reverence, contemplation, Gerald Brom-inspired, avant-garde hairstyle, short dress, math equations print, red flower, night setting.designed by GoBi &Наталья И-ва
  • Using base image: No
  • Aspect Ratio: square

Mystery of the Cosmic Examiner Unveiled

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• Size: 1536 X 1536 (2.36 MP)

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  • Prompt: close-up faceless silhouette with burning symbols "+" and "-" in eye-sockets double exposure with math class exam in school where no one is know the solution of math formula, math symbols and formulas flowing around with thunder lightings, dark ethereal surreal horror art, dark surrealism, hyperdetailed, elegant, glowing and sparkling, hooded being, no-face, empty eye-sockets, focus on a person standing before a junction, mathematical equations, stars, galaxy, fireflies; inspired by Bosch, Blake, Hugo Simberg
  • Using base image: No
  • Aspect Ratio: square