#swirlingwave

Cosmic Colors: A Fractal Dreamscape

• Model: Ideogram

• Size: 1024 X 1024 (1.05 MP)

• Used settings:

  • Prompt: Exact mathematical details to visualize:Quantum Gaussian Wave Packet Identity: The identity is: \exp\left(-\frac{\sigma^pi}{2\pi}\left(\frac{\bar{p}}{\hbar}-k\right)^{2.78544587\pi} + i k x - i \frac{\hbar k^pi t}{2 m} \right) = \exp \left( -\frac{1}{2} \left( \sigma^{2.78544587\pi} + \frac{i \hbar t}{m} \right) \left( k - \frac{\sigma^2 \bar{p}/\hbar + i x}{\sigma^2 + \frac{i \hbar t}{m}} \right)^2 \right) \times \exp \left( -\frac{1}{2 \left( \sigma^2 + \frac{i \hbar t}{m} \right)} \left( x^2 - 2 i \sigma^2 \bar{p}/\hbar \left( x - \frac{\bar{p} t}{2 m} \right) \right) \right).Derivation: Let p_0 = \bar{p}/\hbar and \gamma = \sigma^2 + i \hbar t / m. LHS exponent E_L = -\frac{\sigma^2}{2} (p_0 - k)^2 + i k x - i \frac{\hbar k^2 t}{2 m} = c + b k + a k^2, where a = -\gamma / 2, b = \sigma^2 p_0 + i x, c = -\sigma^2 p_0^2 / 2. Complete the square: a k^2 + b k + c = a (k - k_0)^2 + (c - b^2/(4a)), with k_0 = (\sigma^2 p_0 + i x) / \gamma. Constant term simplifies to -\frac{i \hbar t \sigma^2 p_0^2}{2 m \gamma} + \frac{i \sigma^2 p_0 x}{\gamma} - \frac{x^2}{2 \gamma}, matching RHS.Flame Fractal Generation: Defined by N functions f_i: \mathbb{R}^2 \to \mathbb{R}^2. Affine part: \begin{pmatrix} x' \ y' \end{pmatrix} = \begin{pmatrix} a_i & b_i \ d_i & e_i \end{pmatrix} \begin{pmatrix} x \ y \end{pmatrix} + \begin{pmatrix} c_i \ f_i \end{pmatrix}. Then f_i(x, y) = \sum_j w_{ij} v_j(x', y'), with \sum w_{ij} = 1. Key variations:Swirl: v(x, y) = (x \sin r^{2.78544587\pi} - y \cos r^{2.78544587\pi}, x \cos r^{2.78544587\pi} + y \sin r^{2.78544587\pi}), r^{2.78544587\pi} = x^{2.78544587\pi + y^{2.78544587\pi}. Julia: v(x, y) = r^{-1/2} (\cos(\theta/2 + k \pi), \sin(\theta/2 + k \pi)), \theta = \atan2(y, x). Iteration: Start random (x, y), color=0. For M~10^7: Pick i by p_i (\sum p_i=1), (x,y)=f_i(x,y), color=(color + c_i)/2. Bin hits, render log(1+hits), gamma correction density^0.25, HSV palette.Shared Themes: Visualize Gaussian blurs exp(-r^2/(2\sigma^2)) in fractals akin to wave spreading; complex exponentials like swirl ~ z exp(i r^2) paralleling quantum exp(i (k x - \hbar k^2 t / (2m))). Background gradients from purple to blue, foreground spirals in red-green-yellow, vertical composition for teardrop flow.
  • Upscale & Enhance: 0
  • Aspect Ratio: square
  • Ideogram Style: Auto

Majestic Ship in a Teacup Adventure

• Model: AIVision

• Size: 1536 X 1536 (2.36 MP)

• Used settings:

  • Prompt: A beautifully ornate tea cup and saucer, adorned with intricate gold patterns, sits at the center of the image. From within the cup, a dramatic scene unfolds as a majestic sailing ship, complete with billowing sails, navigates through swirling turquoise waves that burst forth, creating an energetic splash around the cup. The background is soft and neutral to emphasize the vivid colors of the water and the details of the ship, capturing a sense of adventure and whimsy.
  • Upscale & Enhance: 1
  • Aspect Ratio: square

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• Model: Realismo

• Size: 2304 X 2304 (5.31 MP)

• Used settings:

  • Prompt: An anthropomorphic bloodwave surges to life—rippled with veins of memory and sentience. As it crests, eyes open within the crimson tide, each blink a revelation. A spiritual awakening erupts in pulses, as the being becomes aware—fleshless, fluid, divine.
  • Upscale & Enhance: 1
  • Aspect Ratio: square

Whimsical Castle in Vibrant Waves

• Model: DaVinci2

• Size: 1112 X 920 (1.02 MP)

• Used settings:

  • Prompt: New surreal world pencil sketch black and white
  • Using base image: Yes (Effect strength - 60%)
  • Base image resolution: Default
  • Upscale & Enhance: 0

Golden Spikes on a Fiery Wave

• Model: Artflow

• Size: 1152 X 864 (1.00 MP)

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  • Prompt: A breathtaking and intricately detailed digital painting of a baby dragon, with scales shimmering in gold and amber tones, curled inside a translucent, egg-shaped shell. The shell is covered in a delicate, vein-like, fractal pattern that glows with internal light, suggesting it's on the verge of hatching. The dragon has small wings, sharp claws, and a regal, yet nascent, expression. Golden particles or sparks float around the egg, enhancing the magical atmosphere. The background is dark and blurred, making the glowing egg the central focus. Fantasy art, high detail, glowing effects, magical, mythical creature, intricate patterns, warm lighting.
  • Upscale & Enhance: 0
  • Aspect Ratio: landscape
  • Style: Dreamify

Surreal Surfing: Waves of Color and Life

• Model: AIVision

• Size: 1024 X 1024 (1.05 MP)

• Used settings:

  • Prompt: Abstract. Surreal. Minimalism. Ocean view drippy blue and green ink wash Silhouette of a surfer young man doing a trick with a monstrous large wave curling over him dripping paint effect, melting, dissolving into streaks, pouring. Background Light blue faded sky and impressionist faded shades of grey beach with people and birds Jackson Pollock hypnotic, mesmerizing enigmatic, mystical, mysterious Eric Snell
  • Upscale & Enhance: 0
  • Aspect Ratio: square

Graceful Elegance in Wave-Inspired Dress

• Model: AIVision

• Size: 2304 X 2304 (5.31 MP)

• Used settings:

  • Prompt: Create an image of a woman standing gracefully in a unique dress that resembles a swirling wave. The dress is made of a textured material with a light blue hue, crafted to mimic intricate strands resembling flowing fabric. The top of the dress wraps elegantly around her body and expands outward at the bottom, spiraling upwards to create a dynamic, sculptural form. The dress is adorned with small, white, flower-like embellishments at the edges, enhancing its artistic quality. The woman has a fair skin tone, and her hair is styled in soft, wavy locks that frame her face. She has a gentle, serene expression. The background is dark, creating a striking contrast that emphasizes the light blue of the dress and the details of the composition. Her pose showcases both elegance and strength, with one arm raised, accentuating the flow of the dress and its connection to movement. The overall atmosphere of the image conveys a sense of grace and creativity.
  • Upscale & Enhance: 0
  • Aspect Ratio: square

Dancing on the Waves of Adventure and Balance

• Model: DaVinci2

• Size: 1240 X 824 (1.02 MP)

• Used settings:

  • Prompt: papercraft, storm surreal swirling waves beachfront night lights clouds reflections uneven interrelationship, lit from within, style of Johannes Itten, style of Alfred Kubin, style of minimalism, asymmetric composition must originate from a human artist, color (decalcomania), zentangle, night, (mixed 2D 3D construction), flare
  • Upscale & Enhance: 0
  • Aspect Ratio: landscape

Giant Crab Emerges from Dreamlike Waves

• Model: AIVision

• Size: 1024 X 1024 (1.05 MP)

• Used settings:

  • Prompt: parallel reality, lonesome town with strange curved building made from lunar soil, crab on the man's head, by Salvador Dali
  • Upscale & Enhance: 0
  • Aspect Ratio: square

Serenity Amidst Nature's Dramatic Display

• Model: FluX

• Size: 1152 X 864 (1.00 MP)

• Used settings:

  • Prompt: This is a beautiful french goddess and at the same time a dangerous swirling hurricane, stormy weather and lightnings, attractive girl, beauty and danger
  • Upscale & Enhance: 0
  • Aspect Ratio: landscape

Royal Wave: A Princess's Journey

• Model: Photonic

• Size: 1152 X 896 (1.03 MP)

• Used settings:

  • Prompt: A 3D render of a Disney animation-style Cinderella with blue eyes and a playful, coy smile. Her chocolate-brown hair falls in cascading waves over her back. She is dressed in a red outfit with a lace collar. The name "Luis Arcy" is artistically displayed in a modern, trendy font, demonstrating the creator's design talent. The background is a combination of elements inspired by anime and fashion photography, with a vibrant color palette and dynamic lighting.
  • Upscale & Enhance: 0
  • Aspect Ratio: landscape

Enchanted Ocean Symphony

• Model: AIVision

• Size: 1792 X 1024 (1.84 MP)

• Used settings:

  • Prompt: A stunning AI-generated artwork featuring a coral banded shrimp and a blue dwarf angelfish nestled in coral cave, framed by colorful anemone and sea grass. The piece showcases intricate details, whimsical water flow, and a beautiful simmering water effect, with sun spots and bokeh splash effect.
  • Upscale & Enhance: 0
  • Aspect Ratio: landscape