Prompt: A highly detailed, photorealistic 3D rendering of a complex radial fractal structure resembling a flower-like Mandelbulb variant with intricate, self-similar petal layers and wavy undulating edges, generated using iterative mathematical transformations in a raymarching shader; the fractal is defined by constants TAU exactly equal to (2.0 * π) * 0.7887 ≈ 4.955 radians for angular periodicity scaling to create asymmetric twisted repetitions instead of full 2π symmetry, controlling approximately 128-256 fold radial petals; POWER exactly 11.24788742 + TAU ≈ 16.203 for amplifying self-similarity through r^POWER scaling in spherical coordinates during iterations; core vector update z = r * vec3(sin(sin(θ)cos(φ) + sin(θ)sin(φ) + cos(φ)), cos(sin(θ)cos(φ) + cos(θ)cos(φ) + cos(θ)), cos(θ)cos(φ)) + p/1.618, where p is the 3D position vector, r = ||p|| its magnitude, θ = atan(p.y, p.x) azimuthal angle, φ = acos(p.z/r) polar angle; incorporating nonlinear warping via trig sums like expr1 = sin(θ)(cos(φ) + sin(φ)) + cos(φ) = sin(θ) * √2 * sin(φ + π/4) + cos(φ) and expr2 = cos(φ) * √2 * sin(θ + π/4) + cos(θ) for phase-shifted higher harmonics introducing bulges and mixing between angles; followed by p = shp(reflect(p, z)) where reflect(p, z) = p - 2 * (p · ẑ) * ẑ with ẑ = z / ||z|| for mirror symmetries creating sharp creases; shp #define shp(x) (exp(x)-exp(-x))/pi
assumed as absolute folding abs(p) or clamping for bounding and discontinuities; r updated to ||z|| per iteration, looping 64 times with escape radius or distance estimate DE(p) = ( 0.6575 * log(r) * exp(1./r) * r / ||dr/dp|| for rendering; visualize the fractal in vibrant metallic gradients of blue, purple, and gold with orbit trap coloring, floating in cosmical void with soft volumetric lighting and depth of field, ultra-detailed textures emphasizing mathematical precision and geometric warping.
Prompt: A highly detailed, photorealistic 3D rendering of a complex radial fractal structure resembling a flower-like Mandelbulb variant with intricate, self-similar petal layers and wavy undulating edges, generated using iterative mathematical transformations in a raymarching shader; the fractal is defined by constants TAU exactly equal to (2.0 * π) * 0.7887 ≈ 4.955 radians for angular periodicity scaling to create asymmetric twisted repetitions instead of full 2π symmetry, controlling approximately 128-256 fold radial petals; POWER exactly 11.24788742 + TAU ≈ 16.203 for amplifying self-similarity through r^POWER scaling in spherical coordinates during iterations; core vector update z = r * vec3(sin(sin(θ)cos(φ) + sin(θ)sin(φ) + cos(φ)), cos(sin(θ)cos(φ) + cos(θ)cos(φ) + cos(θ)), cos(θ)cos(φ)) + p/1.618, where p is the 3D position vector, r = ||p|| its magnitude, θ = atan(p.y, p.x) azimuthal angle, φ = acos(p.z/r) polar angle; incorporating nonlinear warping via trig sums like expr1 = sin(θ)(cos(φ) + sin(φ)) + cos(φ) = sin(θ) * √2 * sin(φ + π/4) + cos(φ) and expr2 = cos(φ) * √2 * sin(θ + π/4) + cos(θ) for phase-shifted higher harmonics introducing bulges and mixing between angles; followed by p = shp(reflect(p, z)) where reflect(p, z) = p - 2 * (p · ẑ) * ẑ with ẑ = z / ||z|| for mirror symmetries creating sharp creases; #define shp(x) (exp(x)-exp(-x))/pi - shp
assumed as absolute folding abs(p) or clamping for bounding and discontinuities; r updated to ||z|| per iteration, looping 64 times with escape radius or distance estimate DE(p) = ( 0.6575 * log(r) * exp (1./r) * r ) / ||dr/dp|| for rendering; visualize the fractal in vibrant metallic gradients of blue, purple, and gold with orbit trap coloring, floating in a dark void with soft volumetric lighting and depth of field, high resolution 4K, ultra-detailed textures emphasizing mathematical precision and geometric warping.
Prompt: A highly detailed, photorealistic 3D rendering of a complex radial fractal structure resembling a flower-like Mandelbulb variant with intricate, self-similar petal layers and wavy undulating edges, generated using iterative mathematical transformations in a raymarching shader; the fractal is defined by constants TAU exactly equal to (2.0 * π) * 0.7887 ≈ 4.955 radians for angular periodicity scaling to create asymmetric twisted repetitions instead of full 2π symmetry, controlling approximately 128-256 fold radial petals; POWER exactly 11.24788742 + TAU ≈ 16.203 for amplifying self-similarity through r^POWER scaling in spherical coordinates during iterations; core vector update z = r * vec3(sin(sin(θ)cos(φ) + sin(θ)sin(φ) + cos(φ)), cos(sin(θ)cos(φ) + cos(θ)cos(φ) + cos(θ)), cos(θ)cos(φ)) + p/1.618, where p is the 3D position vector, r = ||p|| its magnitude, θ = atan(p.y, p.x) azimuthal angle, φ = acos(p.z/r) polar angle; incorporating nonlinear warping via trig sums like expr1 = sin(θ)(cos(φ) + sin(φ)) + cos(φ) = sin(θ) * √2 * sin(φ + π/4) + cos(φ) and expr2 = cos(φ) * √2 * sin(θ + π/4) + cos(θ) for phase-shifted higher harmonics introducing bulges and mixing between angles; followed by p = shp(reflect(p, z)) where reflect(p, z) = p - 2 * (p · ẑ) * ẑ with ẑ = z / ||z|| for mirror symmetries creating sharp creases; shp #define shp(x) (exp(x)-exp(-x))/pi
assumed as absolute folding abs(p) or clamping for bounding and discontinuities; r updated to ||z|| per iteration, looping 8-20 times with escape radius or distance estimate DE(p) ≈ 0.5 * log(r) * r / ||dr/dp|| for rendering; visualize the fractal in vibrant metallic gradients of blue, purple, and gold with orbit trap coloring, floating in a dark void with soft volumetric lighting and depth of field, high resolution 4K, ultra-detailed textures emphasizing mathematical precision and geometric warping.
Prompt: A highly detailed, photorealistic 3D rendering of a complex radial fractal structure resembling a flower-like Mandelbulb variant with intricate, self-similar petal layers and wavy undulating edges, generated using iterative mathematical transformations in a raymarching shader; the fractal is defined by constants TAU exactly equal to (2.0 * π) * 0.7887 ≈ 4.955 radians for angular periodicity scaling to create asymmetric twisted repetitions instead of full 2π symmetry, controlling approximately 12-16 fold radial petals; POWER exactly 11.24788742 + TAU ≈ 16.203 for amplifying self-similarity through r^POWER scaling in spherical coordinates during iterations; core vector update z = r * vec3(sin(sin(θ)cos(φ) + sin(θ)sin(φ) + cos(φ)), cos(sin(θ)cos(φ) + cos(θ)cos(φ) + cos(θ)), cos(θ)cos(φ)) + p, where p is the 3D position vector, r = ||p|| its magnitude, θ = atan(p.y, p.x) azimuthal angle, φ = acos(p.z/r) polar angle; incorporating nonlinear warping via trig sums like expr1 = sin(θ)(cos(φ) + sin(φ)) + cos(φ) = sin(θ) * √2 * sin(φ + π/4) + cos(φ) and expr2 = cos(φ) * √2 * sin(θ + π/4) + cos(θ) for phase-shifted higher harmonics introducing bulges and mixing between angles; followed by p = shp(reflect(p, z)) where reflect(p, z) = p - 2 * (p · ẑ) * ẑ with ẑ = z / ||z|| for mirror symmetries creating sharp creases; shp #define shp(x) (exp(x)-exp(-x))/pi
assumed as absolute folding abs(p) or clamping for bounding and discontinuities; r updated to ||z|| per iteration, looping 8-20 times with escape radius or distance estimate DE(p) ≈ 0.5 * log(r) * r / ||dr/dp|| for rendering; visualize the fractal in vibrant metallic gradients of blue, purple, and gold with orbit trap coloring, floating in a dark void with soft volumetric lighting and depth of field, high resolution 4K, ultra-detailed textures emphasizing mathematical precision and geometric warping.
Prompt: A highly detailed, abstract 3D fractal rendering resembling a Mandelbulb variant with hyperbolic deformations, featuring a central orange bulbous orb surrounded by swirling, fluid-like lobes in shades of blue, pink, and yellow with iridescent, reflective surfaces and gradient transitions. The fractal is defined iteratively in \(\mathbb{R}^3\) for a point \(\mathbf{c} = (x_0, y_0, z_0)\), starting with \(\mathbf{z}_0 = \mathbf{0}\) or \(\mathbf{z}_0 = \mathbf{c}\), and iterating \(\mathbf{z}_{k+1} = r \cdot \vec3\left( \frac{e^{\cos \theta} - e^{-\cos \theta}}{\pi} \cos \phi, \cos \theta \sin \phi, \cos \theta \right) + \vec3\left( \frac{e^{p_x} - e^{-p_x}}{\pi} p_x, \frac{e^{p_y} - e^{-p_y}}{\pi} p_y, \frac{e^{p_z} - e^{-p_z}}{\pi} p_z \right)\), where \(r = \|\mathbf{z}_k\|\), \(\theta = \arccos\left( \frac{z_k \cdot z}{r} \right)\), \(\phi = \atantwo(z_k.y, z_k.x)\), and \(\mathbf{p}\) is a vector parameter like \(\mathbf{c}\). For higher powers n (e.g., 8), scale to \(r^n\), \(n \theta\), \(n \phi\). Iteration halts if \(r > 4\) or after 50 max iterations. Render using ray marching with distance estimator \(DE(\mathbf{q}) = 0.5 \cdot \frac{\log r \cdot r}{dr}\), surface normals via gradients, Phong/PBR shading with reflections, ambient occlusion, and coloring via orbit traps or escape time mapped to hues (orange for low iterations, blue-pink gradients for higher). Apply post-processing for anti-aliasing, depth-of-field, and glow to achieve a dreamy, metallic sheen, viewed zoomed into the central orb with asymmetric swirling arms.
Prompt: A highly detailed 3D rendering of the quintic Calabi-Yau 3-fold hypersurface in ℂℙ⁴ defined by ∑_{i=0}^4 z_i^5 = 0, a compact complex manifold of complex dimension 3 with trivial canonical bundle K_X ≅
Prompt: A highly detailed 3D rendering of the quintic Calabi-Yau 3-fold hypersurface in ℂℙ⁴ defined by ∑_{i=0}^4 z_i^5 = 0, a compact complex manifold of complex dimension 3 with trivial canonical bundle K_X ≅
Prompt: Generate a highly detailed, abstract 3D fractal rendering resembling a Mandelbulb variant with hyperbolic deformations, featuring a central orange bulbous orb surrounded by swirling, fluid-like lobes in shades of blue, pink, and yellow with iridescent, reflective surfaces and gradient transitions. The fractal is defined iteratively in \(\mathbb{R}^3\) for a point \(\mathbf{c} = (x_0, y_0, z_0)\), starting with \(\mathbf{z}_0 = \mathbf{0}\) or \(\mathbf{z}_0 = \mathbf{c}\), and iterating \(\mathbf{z}_{k+1} = r \cdot \vec3\left( \frac{e^{\cos \theta} - e^{-\cos \theta}}{\pi} \cos \phi, \cos \theta \sin \phi, \cos \theta \right) + \vec3\left( \frac{e^{p_x} - e^{-p_x}}{\pi} p_x, \frac{e^{p_y} - e^{-p_y}}{\pi} p_y, \frac{e^{p_z} - e^{-p_z}}{\pi} p_z \right)\), where \(r = \|\mathbf{z}_k\|\), \(\theta = \arccos\left( \frac{z_k \cdot z}{r} \right)\), \(\phi = \atantwo(z_k.y, z_k.x)\), and \(\mathbf{p}\) is a vector parameter like \(\mathbf{c}\). For higher powers n (e.g., 16), scale to \(r^n\), \(n \theta\), \(n \phi\). Iteration halts if \(r > 4\) or after 50 max iterations. Render using ray marching with distance estimator \(DE(\mathbf{q}) = 0.75 \cdot \frac{\log r \cdot r}{dr}\), surface normals via gradients, Phong/PBR shading with reflections, ambient occlusion, and coloring via orbit traps or escape time mapped to hues (orange for low iterations, blue-pink gradients for higher). Apply post-processing for anti-aliasing, depth-of-field, and glow to achieve a dreamy, metallic sheen, viewed zoomed into the central orb with asymmetric swirling arms.
Prompt: A highly detailed 3D rendering of the quintic Calabi-Yau 3-fold hypersurface in ℂℙ⁴ defined by ∑_{i=0}^4 z_i^5 = 0, a compact complex manifold of complex dimension 3 with trivial canonical bundle K_X ≅
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.
