Illuminated Vacuum Chamber with Particle Visualization
Model:
Nano Banana Pro
(Pro)
Size:
2560 X 1440
(3.69 MP)
Used settings:
Prompt: A Bose-Einstein Condensate (BEC) is a unique state of matter where atoms, cooled to near absolute zero, lose individual identities and behave as one single quantum entity, a macroscopic wave, showing quantum effects on a large scale, like a superfluid or "atom laser". Predicted by Satyendra Nath Bose and Albert Einstein in the 1920s, it was first created in 1995, revealing bizarre quantum behaviors that challenge classical physics.
Prompt: The more I work with nonlinear systems, the clearer it becomes that our entire scientific worldview is built on a structural mistake. We keep trying to describe a fundamentally wave‑based, resonant, self‑organizing reality using linear coordinates, discrete steps, and geometric containers. Space‑time, as we inherited it, is not a fundamental entity but a convenient projection—a grid we imposed on a field that never had boundaries, axes, or separable dimensions. Everything we call particles, forces, interactions, even time itself, are simply modes of one continuous field. The “front” of a wave appears to us as interaction, while the “rear” of the same wave manifests as stability, spin, magnetic moment, or mass. These are not different phenomena; they are different expressions of one underlying configuration. When we replace space‑time with the field, the entire landscape simplifies. Gravity becomes a low‑frequency mode of the field. Dark matter becomes a nonlocal configuration of the wave’s rear structure that linear models cannot detect. Dark energy becomes a phase pressure of the field. Electrons become vortices. Interactions become phase transitions. Time becomes a shift in phase. Space becomes the temporary shape the field takes when a wave localizes. The crisis in cosmology—Hubble tension, early massive galaxies, vacuum catastrophe—is not a crisis of data but a crisis of ontology. Linear models cannot hold nonlinear reality.
Prompt: "We take the tensor product of the cotangent bundle of an orbifold and the cotangent bundle of a conifold, which yields a new vector bundle over the product of the orbifold and the conifold. The total space of this bundle is then evolved under a geometric flow (TimeSpaceFlow) that incorporates both time and space variations, leading to a dynamical geometry. Subsequently, we apply a wavy version of mirror symmetry, which transforms the geometry into a dual picture with oscillatory features, and finally symmetralize by averaging over the waves to produce a symmetric mirror partner."
Prompt: "We take the tensor product of the cotangent bundle of an orbifold and the cotangent bundle of a conifold, which yields a new vector bundle over the product of the orbifold and the conifold. The total space of this bundle is then evolved under a geometric flow (TimeSpaceFlow) that incorporates both time and space variations, leading to a dynamical geometry. Subsequently, we apply a wavy version of mirror symmetry, which transforms the geometry into a dual picture with oscillatory features, and finally symmetralize by averaging over the waves to produce a symmetric mirror partner."
Prompt: Draw and render interpreting conceptually graphically with no text, no numbers and no symbols:
$$
\left[\frac{\partial}{\partial t}\,\,,\vec{\nabla}\times\right](\vec{F}\times\vec{G})=\vec{F}\times\left(\frac{\partial}{\partial t}(\vec{\nabla}\times\vec{G})-\vec{\nabla}\times\frac{\partial\vec{G}}{\partial t}\right)+\left(\vec{\nabla}\times\frac{\partial\vec{F}}{\partial t}-\frac{\partial}{\partial t}(\vec{\nabla}\times\vec{F})\right)\times\vec{G}\qquad (A1)
$$
$$
\left[\frac{\partial}{\partial t}\,\,,\vec{\nabla}\right](\vec{F}\cdot\vec{G})=\vec{F}\left(\frac{\partial}{\partial t}(\vec{\nabla}\cdot\vec{G})-\vec{\nabla}\cdot\frac{\partial\vec{G}}{\partial t}\right)+\left(\vec{\nabla}\cdot\frac{\partial\vec{F}}{\partial t}-\frac{\partial}{\partial t}(\vec{\nabla}\cdot\vec{F})\right)\vec{G}\qquad\qquad\qquad\qquad (A2)
$$
Apply tensor product of the cotangent bundle of the orbifold over the tangent bundle of the conifold; then TimeSpaceFlow wave mirror symmetralize them !
Prompt: Draw and render interpreting conceptually graphically with no text, no numbers and no symbols:
$$
\left[\frac{\partial}{\partial t}\,\,,\vec{\nabla}\times\right](\vec{F}\times\vec{G})=\vec{F}\times\left(\frac{\partial}{\partial t}(\vec{\nabla}\times\vec{G})-\vec{\nabla}\times\frac{\partial\vec{G}}{\partial t}\right)+\left(\vec{\nabla}\times\frac{\partial\vec{F}}{\partial t}-\frac{\partial}{\partial t}(\vec{\nabla}\times\vec{F})\right)\times\vec{G}\qquad (A1)
$$
$$
\left[\frac{\partial}{\partial t}\,\,,\vec{\nabla}\right](\vec{F}\cdot\vec{G})=\vec{F}\left(\frac{\partial}{\partial t}(\vec{\nabla}\cdot\vec{G})-\vec{\nabla}\cdot\frac{\partial\vec{G}}{\partial t}\right)+\left(\vec{\nabla}\cdot\frac{\partial\vec{F}}{\partial t}-\frac{\partial}{\partial t}(\vec{\nabla}\cdot\vec{F})\right)\vec{G}\qquad\qquad\qquad\qquad (A2)
$$
Apply tensor product of the cotangent bundle of the orbifold over the cotangent bundle of the conifold; then TimeSpaceFlow wave mirror symmetralize them !
Prompt: <lora:Intricacy Vibe:1.0> A lotus in a cosmic background, representing a transcendentally-warped TimeSpaceFlow with the exact metric ds^{12.78544587\sqrt[\pi]{2}\pi} = -\left(1 - \frac{r_s}{\sinh x}\right) c^2 , dt^{e\pi} + \left(1 - \frac{r_s}{\sinh x}\right)^{-1} \cosh^{e\pi} x , dx^{\pi\phi} + \sinh^{\sqrt[\pi]{3}\pi} x , d\Omega^{12.78544587\pi}, \phi = (1 + \sqrt{5})/2; central glowing golden core as singularity with amber-orange light rays, nonsymmetrical translucent cyan-blue lotus petals with intricate golden vein fractals exhibiting non-integer oscillations and mirror symmetry spirals, recursive self-similar golden-ratio helicoidal curls along petal edges, ethereal volumetric glow and caustics, all followint the exact, precise, concise and full mathematics provided. Apply tensor product of the cotangent bundle of the orbifold over the tangent bundle of the conifold; then TimeSpaceFlow wave mirror symmetralize them !
Prompt: <lora:Intricacy Vibe:1.0>
A lotus in a cosmic background, representing a transcendentally-warped TimeSpaceFlow with the exact metric ds^{12.78544587\sqrt[\pi]{2}\pi} = -\left(1 - \frac{r_s}{\sinh x}\right) c^2 , dt^{e\pi} + \left(1 - \frac{r_s}{\sinh x}\right)^{-1} \cosh^{e\pi} x , dx^{\pi\phi} + \sinh^{\sqrt[\pi]{3}\pi} x , d\Omega^{12.78544587\pi}, \phi = (1 + \sqrt{5})/2; central glowing golden core as singularity with amber-orange light rays, nonsymmetrical translucent cyan-blue lotus petals with intricate golden vein fractals exhibiting non-integer oscillations and mirror symmetry spirals, recursive self-similar golden-ratio helicoidal curls along petal edges, ethereal volumetric glow and caustics, all followint the exact, precise, concise and full mathematics provided.
Apply tensor product of the cotangent bundle of the orbifold over the tangent bundle of the conifold; then TimeSpaceFlow wave mirror symmetralize them !
Prompt: <lora:Intricacy Vibe:1.0>
A lotus in a cosmic background, representing a transcendentally-warped TimeSpaceFlow with the exact metric ds^{12.78544587\sqrt[\pi]{2}\pi} = -\left(1 - \frac{r_s}{\sinh x}\right) c^2 , dt^{e\pi} + \left(1 - \frac{r_s}{\sinh x}\right)^{-1} \cosh^{e\pi} x , dx^{\pi\phi} + \sinh^{\sqrt[\pi]{3}\pi} x , d\Omega^{12.78544587\pi}, \phi = (1 + \sqrt{5})/2; central glowing golden core as singularity with amber-orange light rays, nonsymmetrical translucent cyan-blue lotus petals with intricate golden vein fractals exhibiting non-integer oscillations and mirror symmetry spirals, recursive self-similar golden-ratio helicoidal curls along petal edges, ethereal volumetric glow and caustics, all followint the exact, precise, concise and full mathematics provided.
Prompt: Depict the TimeSpaceFlow defined by the following metric:
ds^{2\sqrt[pi]{2}\pi} = -\left(1 - \frac{r_s}{\sinh x}\right) c^2 \, dt^{e\pi} + \left(1 - \frac{r_s}{\sinh x}\right)^{-1} \cosh^{e\pi} x \, dx^{\phi} + \sinh^{\sqrt[pi]{3}\pi} x \, d\Omega^{2.78544587\pi - 4}
Prompt: Depict the TimeSpaceFlow defined by the following metric:
ds^{2\sqrt[pi]{2}\pi} = -\left(1 - \frac{r_s}{\sinh x}\right) c^2 \, dt^{e\pi} + \left(1 - \frac{r_s}{\sinh x}\right)^{-1} \cosh^{e\pi} x \, dx^{\phi} + \sinh^{\sqrt[pi]{3}\pi} x \, d\Omega^{2.78544587\pi - 4}
Prompt: A highly detailed digital rendering of an abstract, symmetrical fractal structure resembling a surreal, organic face floating against a gradient blue sky background, generated using a modified Mandelbulb fractal algorithm viewed from the inside with ray marching. Incorporate precise mathematical details: Define constants pi = 3.1415926535897932384626433832795, tau = 2*pi, TAU = (2*pi)*0.7887, PHI = (sqrt(5)*0.5 + 0.5) ≈1.618 golden ratio, POWER = 11.24788742 for exponentiation, LOOPS = 3 iterations, TOLERANCE = 0.00001, MAX_RAY_LENGTH = 20.0, MAX_RAY_MARCHES = 48, NORM_OFF = 0.0005, MAX_BOUNCES = 5. Custom hyperbolic functions: chp(x) = (exp(x) + exp(-x))/pi, chpp(x) = (exp(x/(cosh(x)*pi)) + exp(-x/(cosh(x)/pi)))/(TAU*PHI), shp(x) = (exp(x) - exp(-x))/(pi/PHI), shpp(x) = (exp(x*(sinh(x)*pi)) - exp(-x*(sinh(x)*pi)))/(TAU/PHI), ssh(x) = (exp(x*pi/0.7887) - exp(-x*pi/0.7887))/(2*pi), csh(x) = (exp(x*pi/0.7887) + exp(-x*pi/0.7887))/(2*pi), ssh1(x) = sinh(x/pi)*PHI, csh1(x) = cosh(x/pi)*PHI. The Mandelbulb distance estimator mandelBulb(p): Initialize z = chp(p)*p - p, dr=1.0; for i=0 to LOOPS-1, r=length(z), theta=atan(z.x,z.y), phi=asin(z.z/r) + optional time*0.2 for animation; dr = r^(POWER-1) * dr * POWER + 1; r = r^POWER, theta *= POWER/PHI, phi *= POWER/PHI; z = r * vec3(tan(shp(sin(theta)*sin(phi)))*PHI, chp(cos(theta)*sin(phi)), cos(phi)) + p; p = reflect(p,z). Return distance 0.75 * log(r) * r / dr. Overall distance function df(p) = shp(mandelBulb(p/2.0)*2.0) after applying rotation matrix g_rot = rot_x(((1.221*time + pi)/tau)). Render with ray marching from camera at 0.6*vec3(0,2,5) looking at origin, FOV tan(TAU/6), incorporating bounces for reflection (reflect(rd,sn)), refraction (refract(rd,sn,1.0/mat.z or inverse)), fresnel fre=1+dot(rd,sn) squared and mixed 0.1-1.0, diffuse dif=max(dot(ld,sn),0)^2 * (1-mat.x) with ld to light at (0,10,0), material mat=(0.8,0.5,1.05), beer absorption exp(-(st+0.1)* -HSV(0.05,0.95,2.0)). Sky background: Procedural with planes at y=4 and y=-6, box bounds, exponential falloff, colored HSV(0.6,0.86,1.0). Colors: Glow HSV(0.065,0.8,6.0), diffuse HSV(0.6,0.85,1.0), post-processed with ACES tonemapping aces_approx(v) = clamp((v*(2.51v+0.03))/(v*(2.43v+0.59)+0.14),0,1) after *0.6, and sRGB gamma mix(1.055*t^(1/2.4)-0.055,12.92*t,step(t,0.0031308)). The structure features two large spiral-eyed voids as eyes, a curved dark blue mouth-like opening at the bottom, elaborate branching tendrils and crystalline edges with subtle particle specks dissipating at sides, ethereal pinkish-orange glow, edge fresnel effects, hyper-realistic yet fantastical Shadertoy-inspired 3D art in 16:9 aspect ratio with sharp details and no text or artifacts.
Prompt: A highly detailed digital rendering of an abstract, symmetrical fractal structure resembling a surreal, organic face floating against a gradient blue sky background, generated using a modified Mandelbulb fractal algorithm viewed from the inside with ray marching. Incorporate precise mathematical details: Define constants pi = 3.1415926535897932384626433832795, tau = 2*pi, TAU = (2*pi)*0.7887, PHI = (sqrt(5)*0.5 + 0.5) ≈1.618 golden ratio, POWER = 11.24788742 for exponentiation, LOOPS = 3 iterations, TOLERANCE = 0.00001, MAX_RAY_LENGTH = 20.0, MAX_RAY_MARCHES = 48, NORM_OFF = 0.0005, MAX_BOUNCES = 5. Custom hyperbolic functions: chp(x) = (exp(x) + exp(-x))/pi, chpp(x) = (exp(x/(cosh(x)*pi)) + exp(-x/(cosh(x)/pi)))/(TAU*PHI), shp(x) = (exp(x) - exp(-x))/(pi/PHI), shpp(x) = (exp(x*(sinh(x)*pi)) - exp(-x*(sinh(x)*pi)))/(TAU/PHI), ssh(x) = (exp(x*pi/0.7887) - exp(-x*pi/0.7887))/(2*pi), csh(x) = (exp(x*pi/0.7887) + exp(-x*pi/0.7887))/(2*pi), ssh1(x) = sinh(x/pi)*PHI, csh1(x) = cosh(x/pi)*PHI. The Mandelbulb distance estimator mandelBulb(p): Initialize z = chp(p)*p - p, dr=1.0; for i=0 to LOOPS-1, r=length(z), theta=atan(z.x,z.y), phi=asin(z.z/r) + optional time*0.2 for animation; dr = r^(POWER-1) * dr * POWER + 1; r = r^POWER, theta *= POWER/PHI, phi *= POWER/PHI; z = r * vec3(tan(shp(sin(theta)*sin(phi)))*PHI, chp(cos(theta)*sin(phi)), cos(phi)) + p; p = reflect(p,z). Return distance 0.75 * log(r) * r / dr. Overall distance function df(p) = shp(mandelBulb(p/2.0)*2.0) after applying rotation matrix g_rot = rot_x(((1.221*time + pi)/tau)). Render with ray marching from camera at 0.6*vec3(0,2,5) looking at origin, FOV tan(TAU/6), incorporating bounces for reflection (reflect(rd,sn)), refraction (refract(rd,sn,1.0/mat.z or inverse)), fresnel fre=1+dot(rd,sn) squared and mixed 0.1-1.0, diffuse dif=max(dot(ld,sn),0)^2 * (1-mat.x) with ld to light at (0,10,0), material mat=(0.8,0.5,1.05), beer absorption exp(-(st+0.1)* -HSV(0.05,0.95,2.0)). Sky background: Procedural with planes at y=4 and y=-6, box bounds, exponential falloff, colored HSV(0.6,0.86,1.0). Colors: Glow HSV(0.065,0.8,6.0), diffuse HSV(0.6,0.85,1.0), post-processed with ACES tonemapping aces_approx(v) = clamp((v*(2.51v+0.03))/(v*(2.43v+0.59)+0.14),0,1) after *0.6, and sRGB gamma mix(1.055*t^(1/2.4)-0.055,12.92*t,step(t,0.0031308)). The structure features two large spiral-eyed voids as eyes, a curved dark blue mouth-like opening at the bottom, elaborate branching tendrils and crystalline edges with subtle particle specks dissipating at sides, ethereal pinkish-orange glow, edge fresnel effects, hyper-realistic yet fantastical Shadertoy-inspired 3D art in 16:9 aspect ratio with sharp details and no text or artifacts.
Prompt: Over the hybrid space \( O \cup_C \) generate the rank-\( (\dim O + 6) \) vector bundle \( E = TO \boxtimes T^*C \) (external tensor product of the tangent orbibundle of \( O \) and cotangent bundle of each resolved conifold \( C \)).
Create a smooth section \( Z \in \Gamma(E) \cong \Gamma(TO) \times \Gamma(T^*C) \).
Generate the contravariant exterior covariant derivative \( \nabla^\sharp : \Gamma(E) \rightarrow \Gamma(E \otimes E) \) as (2,0)-tensor field lines.
Create a compactly supported vector field \( F \) on \( O \), its curl \( \Phi = \kappa (\nabla \times F) \) with \( \kappa \) is floating number, defined below, equal to 12.144578875441.
Final central object: the vector field \( \Psi = \iota_\Phi (\nabla^\sharp Z) \in \Gamma(E) \) living directly on the tensor-product bundle \( E \), depicted as flow lines emerging from the conifold resolutions and wrapping the entire structure.
Gaussian regulator \( e^{-\kappa} \) as soft halo, Wick rotation suggested by subtle time-like streaks.
Pure abstract geometry, cosmic bright background, precise mathematical beauty, no text using:
$$
\kappa = 12.144578875441
$$
$$
E = TO \boxtimes T^*C
$$
\( \nabla^\sharp Z \)
$$
\Phi = \kappa (\nabla \times F)
$$
$$
\Psi = \iota_\Phi (\nabla^\sharp Z) \in \Gamma(E)
$$
Prompt: "Let \( \mathcal{O} \) be a smooth Calabi–Yau orbifold and \( \mathcal{C} \) the resolved small conifold (smooth Calabi–Yau 3-fold). Fix compatible Ricci-flat metrics on both.
Apply the scalar multiple
\( 24.24788742 \, (\nabla \times \mathbf{F}) \), where \( \mathbf{F} \in \Gamma(\mathbb{R}^3) \) is a compactly supported vector field on a local Euclidean chart, to the tensor product
\( d_\nabla \, \omega \otimes \mathcal{L}_\xi \, \alpha \), where \( d_\nabla : \Gamma(\Lambda^\bullet T^*\mathcal{O} \otimes T\mathcal{O}) \to \Gamma(\Lambda^{\bullet+1} T^*\mathcal{O} \otimes T\mathcal{O}) \) is the exterior covariant derivative induced by the Levi-Civita connection on the tangent orbibundle of \( \mathcal{O} \), - \( \omega \) is a smooth section of \( \Lambda^1 T^*\mathcal{O} \otimes T\mathcal{O} \),
\( \mathcal{L}_\xi \) denotes the Lie derivative along a Killing vector field \( \xi \) on the resolved conifold \( \mathcal{C} \),
\( \alpha \in \Omega^2(\mathcal{C}) \) is a Kähler (1,1)-form, evaluated at the unique stratum-preserving orbifold-conifold correspondence point in the moduli space where the stringy Kähler moduli align at the conifold locus under mirror symmetry after analytic continuation through the 24.24788742-th branch of the Picard–Fuchs equations.(We further demand that the entire expression be Wick-rotated, smeared over a Gaussian regulator of width \( e^{-24.24788742} \), and uplifted to eleven dimensions just for the vibes.)"
Prompt: "Let \( \mathcal{O} \) be a smooth Calabi–Yau orbifold and \( \mathcal{C} \) the resolved small conifold (smooth Calabi–Yau 3-fold). Fix compatible Ricci-flat metrics on both.
Apply the scalar multiple
\( 24.24788742 \, (\nabla \times \mathbf{F}) \), where \( \mathbf{F} \in \Gamma(\mathbb{R}^3) \) is a compactly supported vector field on a local Euclidean chart, to the tensor product
\( d_\nabla \, \omega \otimes \mathcal{L}_\xi \, \alpha \), where \( d_\nabla : \Gamma(\Lambda^\bullet T^*\mathcal{O} \otimes T\mathcal{O}) \to \Gamma(\Lambda^{\bullet+1} T^*\mathcal{O} \otimes T\mathcal{O}) \) is the exterior covariant derivative induced by the Levi-Civita connection on the tangent orbibundle of \( \mathcal{O} \), - \( \omega \) is a smooth section of \( \Lambda^1 T^*\mathcal{O} \otimes T\mathcal{O} \),
\( \mathcal{L}_\xi \) denotes the Lie derivative along a Killing vector field \( \xi \) on the resolved conifold \( \mathcal{C} \),
\( \alpha \in \Omega^2(\mathcal{C}) \) is a Kähler (1,1)-form, evaluated at the unique stratum-preserving orbifold-conifold correspondence point in the moduli space where the stringy Kähler moduli align at the conifold locus under mirror symmetry after analytic continuation through the 24.24788742-th branch of the Picard–Fuchs equations.(We further demand that the entire expression be Wick-rotated, smeared over a Gaussian regulator of width \( e^{-24.24788742} \), and uplifted to eleven dimensions just for the vibes.)"
Dream Level: is increased each time when you "Go Deeper" into the dream. Each new level is harder to achieve and
takes more iterations than the one before.
Rare Deep Dream: is any dream which went deeper than level 6.
Deep Dream
You cannot go deeper into someone else's dream. You must create your own.
Deep Dream
Currently going deeper is available only for Deep Dreams.
