#symmetry

Exploring Intricate 3D Mathematical Patterns

• Model: AIVision

• Size: 1536 X 1536 (2.36 MP)

• Used settings:

  • 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.)"
  • Using base image: No
  • Aspect Ratio: square

3D Structures with Complex Mathematical Forms

• Model: AIVision

• Size: 1536 X 1536 (2.36 MP)

• Used settings:

  • Prompt: 3D structures with forms, generated using vec3 z = π * p / (exp(p) + exp(-p)) - p / Φ^n with n = 0 to 64, incorporating chp(x) = (exp(x) + exp(-x))/π, chpp(x) = (exp(x/(cosh(x)·π)) + exp(-x/(cosh(x)/π)))/(2π·Φ), shp(x) = (exp(x) - exp(-x))/π, shpp(x) = 1/(exp(x·sinh(x)·π) - exp(-x·sinh(x)·π))/(2π·Φ), ssh(x) = (exp(x·π/.7887) - exp(-x·π/.7887))/(2π), csh(x) = (exp(x·π/.7887) + exp(-x·π/.7887))/(2π), ssh1(x) = sinh(x/π)/Φ, csh1(x) = cosh(x/π)/Φ, with high symmetry, golden ratio scaling (Φ = (1 + √5)/2), and logarithmic refinement z *= -π·log(||z||), enhanced by additional transforms: z += sin(τ·||z||)·p/||p|| for oscillatory perturbation, z = z / (1 + ||z||^2) for projective normalization, z = z + Φ^(-n)·cross(p, z) for rotational twist, z *= exp(-||z||/τ) for exponential decay, z = z + ∇(cosh(||p||)·sin(π·||z||)) for gradient-based modulation, and the new spherical transform z = r * (vec3(tan(shp(sin(θ)*sin(φ)))*Φ, chp(cos(θ)*sin(φ)), cos(φ))) + p where θ and φ are angular coordinates, r is a radial scale, and p is the input vector, showcasing iterative variants. Apply 64.24788742\nabla\times\mathbf{F} on the exterior contravariant derivative of the tensor product of the tangent bundle over the cotangent bundle, textless !
  • Using base image: No
  • Aspect Ratio: square

Intricate Orange and Turquoise Mandala Art

• Model: DaVinci2

• Size: 1024 X 1024 (1.05 MP)

• Used settings:

  • Prompt: A vibrant, intricate mandala design featuring layers of orange, blue, and teal petals. The symmetrical patterns create a mesmerizing, harmonious visual that draws the eye inward, Kundun
  • Using base image: No
  • Aspect Ratio: square

Elegant Black-and-White Snowflake Design

• Model: DaVinci2

• Size: 1152 X 864 (1.00 MP)

• Used settings:

  • Prompt: snowflake zentangle
  • Using base image: No
  • Aspect Ratio: landscape

Elegant Floral Patterns in Symmetrical Design

• Model: MirageMaker

• Size: 768 X 768 (0.59 MP)

• Used settings:

  • Prompt: Congolese rainforest animals medieval manuscript scaly scales
  • Using base image: No
  • Aspect Ratio: square

Hypnotic Symmetry in Abstract Design

• Model: Photonic

• Size: 1536 X 1536 (2.36 MP)

• Used settings:

  • Prompt: A minimalist geometric illustration featuring a series of concentric circles that gradually decrease in size from the outer edge toward the center. Each circle is rendered in progressively lighter shades of deep navy blue, creating a hypnotic spiral effect that draws the eye inward. The circles are perfectly aligned and evenly spaced, with crisp, clean lines against a stark white background. The composition suggests infinite recession and mathematical precision, evoking a sense of meditative depth and visual rhythm.
  • Using base image: No
  • Aspect Ratio: square

Ken Has Reached Zen

• Model: AIVision

• Size: 2880 X 2880 (8.29 MP)

• Used settings:

  • Prompt: Create an intricate black-and-white psychedelic background filled with swirling, twisting patterns of varying textures — spirals, waves, fractals, and sacred geometric forms merging into an infinite, maze-like environment. In the center, depict a person in a sitting lotus position with their elbows resting on their knees, hands outward placing the tip of the thumb and index finger together while keeping the other fingers extended as if reaching nirvana through meditation. The person’s expression should radiate awe, transcendence, and ecstatic realization — eyes heavy with wonder, mouth in a sublime smile slightly open in breathless amazement. Their skin should be covered in vivid, rainbow-colored patterns of concentric circles and flowing designs, resembling bioluminescent body paint or sacred tattoos awakening with energy. The same colorful pattern should seamlessly extend into their clothing, symbolizing unity between body, spirit, and the infinite design around them. Their hair can either blend into the patterns or glow subtly, emphasizing harmony with the surrounding energy. The composition should evoke the moment of psychedelic awakening — where consciousness expands and dissolves into the living geometry of existence. The scene should feel radiant, visionary, and deeply interconnected, overflowing with surreal detail and visual complexity.
  • Using base image: No
  • Aspect Ratio: square

Mandala of Harmony

• Model: Artistic

• Size: 1920 X 1920 (3.69 MP)

• Used settings:

  • Prompt: cornucopia,
  • Using base image: No
  • Aspect Ratio: square

Intricate Black and White Mandala Design

• Model: DaVinci2

• Size: 1152 X 864 (1.00 MP)

• Used settings:

  • Prompt: zentangle SOUL
  • Using base image: No
  • Aspect Ratio: landscape

Vibrant Stained Glass Design Masterpiece

• Model: DaVinci2

• Size: 2024 X 1136 (2.30 MP)

• Used settings:

  • Prompt: Vibrant stained glass window, intricate geometric patterns, rich jewel tones, sunlight filtering through, cathedral setting, historical religious motifs, detailed craftsmanship, glowing colors, illuminated panels, intricate leadwork, spiritual ambiance, traditional artistry, medium: digital illustration, high resolution, dramatic lighting effects, luminous blues, reds, greens, and golds.
  • Using base image: No
  • Aspect Ratio: landscape

Ethereal Fractal Glow: A Symmetrical Journey

• Model: AIVision

• Size: 1536 X 1536 (2.36 MP)

• Used settings:

  • Prompt: An image of a highly detailed, symmetrical 3D fractal structure exhibiting translucent, refractive qualities, internal amber-tinted glow from Beer-Lambert absorption using high-contrast ethereal vibrancy achieved via ray marching with tolerance 0.00001, max ray length 748.0, up to 748 marches, and 16 bounces for reflections and refractions, starting from camera at (1.256,2.47855874,-7.5) looking at origin with FOV tan(tau/16.61) where tau=2*pi. The distance field df(p) = shp(mandelBulb(p/z1)*z1) with z1=2.0, where shp(x) = (exp(x)-exp(-x))/(pi/PHI) and PHI=(sqrt(5)/2 + 0.5)≈1.618.The mandelBulb(p) function iterates with power=11.24788742 and loops=16: initialize z = chp(p)*p - p where chp(x)=(exp(x)+exp(-x))/pi; dr=1.0; for each loop, r=length(z), bail if r>2; theta=atan(z.x,z.y); phi=acos(z.z/r) + asinh(time)*0.2; dr = pow(r,power-1)*dr*power +1; r=pow(r,power); theta*=power/PHI; phi*=power/PHI; z = r * vec3(tan(shp(sin(theta)*sin(phi)))/(PHI*tau), chp(cos(theta)*sin(phi))/(PHI*tau), (cos(phi)*sin(phi))/(PHI*tau)) + p; p=reflect(p,z); return 0.75*log(r)*r/dr.Incorporate custom hyperbolic functions for distortions: chpp(x)=(exp(x/(cosh(x)*pi))+exp(-x/(cosh(x)/pi)))/(TAU*PHI) with TAU=(2*pi)*0.7887≈4.951; 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. Use these in skyColor with reflections as reflect(-ssh1(rd), chpp(ro)), in rendering aggregation as agg += ssh1(ragg*skyColor(ro,rd)), and ray updates as rd=chpp(ref) or ro=shpp(sp + initt*rd) with initt=0.1.Material properties: mat=vec3(0.8,0.5,1.05) for diffuse, specular, refractive index; Fresnel fre=1+dot(rd,sn), fre*=fre, mix(0.1,1,fre); diffuse col += diffuseCol * dif*dif *(1-mat.x) with dif=max(dot(ld,sn),0), ld=normalize(lightPos-sp), lightPos=(0,10,0); reflection col += rsky*mat.y*fre*vec3(1)*edge with edge=smoothstep(1,0.9,fre); colors from HSV: skyCol=HSV(0.6,0.86,1), glowCol=HSV(0.065,0.8,6), diffuseCol=HSV(0.6,0.85,1). Inside traversal flips dfactor=-1, applies absorption ragg *= exp(-(st+initt)*beer), and refracts with index 1/mat.z when inside.Normals computed via finite differences: nor.x = df(pos+eps.xyy)-df(pos-eps.xyy) etc., with eps=(0.0005,0). Sky includes ray-plane intersections tp=(dot(ro,p.xyz)+p.w)/dot(rd,p.xyz) for planes at y=4 and y=-6, with box(pp,vec2(6,9))-1 for patterns, col += 4*skyCol*rd.y*rd.y*smoothstep(0.25,0,db) + 0.8*skyCol*exp(-0.5*max(db,0)), and similar for circular ds=length(pp)-0.5, clamped and shaped with shp(clamp(col,0,10)).Match the visual style of a Shadertoy-generated "Inside the Mandelbulb II" fractal art piece, capturing a static frame of the animated, lucky-bug emergent symmetry from reflections and custom coordinate remaps for asymmetric flaring in protrusions, explosive tan-amplified edges, and harmonic golden-ratio scalings.
  • Using base image: No
  • Aspect Ratio: square

Majestic Lion: A Masterpiece of Illusion

• Model: FluX

• Size: 2981 X 1677 (5.00 MP)

• Used settings:

  • Prompt: A majestic lion adorned with mesmerizing patterns and tattoos, an optical illusion masterpiece, intricate and diverse pattern line work, showcasing symmetry, precision, and perfectionism in the style of MC Escher, Marcel Duchamp, Peter Kogler, and Picasso. The lion features symmetrical wide-set eyes with irises farther apart than the center, creating an elegant and surreal look. The image is captured through award-winning photography in a bright studio setting, ensuring every detail is highlighted. The resolution is set at 8k to emphasize the cinematic quality, with lighting that adds a golden touch to the composition. The artwork is hyperrealistic, ultra-detailed, and of the highest definition, with crisp quality and cinematic post-processing enhancing the Cubism-inspired design.
  • Using base image: No
  • Aspect Ratio: landscape_wide

Fiery Orange Iris in Dark Contrast

• Model: DreamForge

• Size: 1152 X 864 (1.00 MP)

• Used settings:

  • Prompt: A reflection of horror on innocent eyes
  • Using base image: No
  • Aspect Ratio: landscape

Vibrant Swirls: A Dance

• Model: DaVinci2

• Size: 1328 X 1728 (2.29 MP)

• Used settings:

  • Prompt: Abstract surrealism, enigmatic layers, human psyche, unconventional techniques, dark psychological depths, vibrant aesthetics, challenging perceptions, thought-provoking, disturbing, colorful details, mysterious symbolism, cosmic textures, ethereal depths, dynamic brushwork, dramatic lighting, vivid color contrasts, high-resolution, cosmic visual odyssey, intricate abstract expressionism.
  • Using base image: Yes

Winter Wonderland

• Model: DaVinci2

• Size: 1728 X 1296 (2.24 MP)

• Used settings:

  • Prompt: Snowly in a winter fairytale land and Christmas details. Patchwork Klimt, Nicoletta Ceccoli, Naoto Hattori, Didier Lourenço, Leonora Carrington
  • Using base image: No
  • Aspect Ratio: landscape

Mystical Women in Vibrant Abstract Art

• Model: DaVinci2

• Size: 1008 X 1024 (1.03 MP)

• Used settings:

  • Prompt: make a surreal abstract artistic composition, of the styles of Scott Bergey, Richard Burlet, and Peter Wileman,
  • Using base image: Yes

Impressive Physique in Dynamic Angles

• Model: DaVinci2

• Size: 1152 X 864 (1.00 MP)

• Used settings:

  • Prompt: * Height: 6’4” * Build: Athletic – Lean, powerfully built, and conditioned by years of military service and tireless travel. His frame is broad-shouldered with defined musculature, not bulky, but possessing a formidable strength and endurance. He moves with a quiet, efficient grace that belies his size. * Hair: Blonde – Thick, practical, often a little dishevelled or sun-bleached from exposure. He keeps it short enough to be out of his way but long enough to show its natural wave. * Eyes: Piercing Blue – Deep-set and intensely observant. They hold a distant, almost mournful quality, reflecting a past filled with hardship and a soul burdened by profound memories. They can narrow with dangerous precision when focused or soften rarely with moments of genuine empathy. * Distinguishing Marks: A faint, jagged scar runs along his left temple, barely visible under his hair – a memento from a skirmish. Another, more prominent, runs across his left forearm, likely from a bayonet or saber. His hands are calloused and strong, his skin weathered by sun and wind.
  • Using base image: No
  • Aspect Ratio: landscape

Blooming Harmony: A Floral Design Journey

• Model: Photonic

• Size: 1024 X 1024 (1.05 MP)

• Used settings:

  • 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.
  • Using base image: No
  • Aspect Ratio: square

Vibrant Floral Swirls in Blue and Magenta

• Model: DaVinci2

• Size: 1152 X 864 (1.00 MP)

• Used settings:

  • Prompt: EXTREME CYMATICS INFRAREDextreme high quality colors and textures.extreme high quality colors extreme beautiful Beauty.extreme 3D high quality effect.extreme visual effects.extreme masterpiece extreme award-winning masterpiece.rich in detail and texture.lavish Rich colors world's greatest AI image ever made.Striking Arresting Conspicuous Noticeable Impressive Spectacular Breathtaking Attention-grabbing high-resolution images, sharp images, crystal-clear pictures A "masterpiece", "magnum opus", "chef-d'oeuvre",crowning achievement"elaborate, intricate, comprehensive, exhaustive, minute, meticulous.Elite award winners:. Top-tier award recipients. Distinguished champions . Renowned award winners. Prize-winning champions. Laureate champions. Acclaimed champions
  • Using base image: No
  • Aspect Ratio: landscape

Futuristic Female Robots in Stunning Gold Design

• Model: DaVinci2

• Size: 1016 X 1016 (1.03 MP)

• Used settings:

  • Prompt: a chirality of molecular structures exhibiting quantum shaped like entanglement with trypophobia-inducing holes.symmetry;bold colors artstation ,Gothic style
  • Using base image: Yes