Prompt: Imagine you have a list of natural numbers (1, 2, 3, 4, ...). Riemann's zeta function takes a number 's' and sums the reciprocals of all the numbers in that list raised to the power of 's'.
For example, zeta(2) = 1/1^2 + 1/2^2 + 1/3^2 + ... (sum of reciprocals of squares of natural numbers).
This function is interesting because it helps solve many problems related to prime numbers, which are the building blocks of all natural numbers. However, the zeta function is not defined for all values of 's'. It gets a bit tricky at 's' = 1.
The trickiness at s = 1 in the Riemann zeta function can be visualized by imagining a teeter-totter:
Think about the sum for zeta(2) again: 1/1^2 + 1/2^2 + 1/3^2 + .... Each term gets smaller and smaller as you go further down the list. This makes the sum well-behaved and eventually converges to a specific value.
But now, imagine s = 1. The sum becomes 1/1 + 1/2 + 1/3 + .... Here, each term is either 1 or bigger than 1. It's like putting only heavy weights on one side of the teeter-totter. The sum keeps getting bigger and bigger, never settling on a specific value. Mathematicians call this situation "divergence."
There are ways to define the zeta function for other values of 's' even though the simple sum diverges at 1. It's like using advanced techniques to balance the teeter-totter so it makes sense even with those heavy weights. But understanding that initial imbalance at s = 1 is the first hurdle.
Prompt: A vibrant, jewel-toned, highly detailed, and polished image with fluid, organic textures, soft and ethereal lighting, and a luminous, dreamlike aesthetic. A mathematical diagram on a black background illustrates Euler's Formula and Euler's Identity, along with a unit circle representation. The formula "e^(iα) = cos α + i sin α" is in bright green text with "Euler's Formula:" aligned vertically to the left. The unit circle in the complex plane is white, with yellow horizontal and vertical arrows labeled "Re" and "Im" respectively. The origin is "0". Points "i" and "e^(iφ) = cos φ + i sin φ" are marked on the unit circle with white dots. A white line extends from the origin to "e^(iφ)". Teal dashed lines project to the axes, labeled "cos φ" and "sin φ". An angle "φ" is marked. At the bottom, "e^(iπ) + 1 = 0" in blue text, with "Euler's Identity:" aligned vertically to the right. The entire scene is set against a teal sphere centered on a black background, encased within two golden circles that intersect vertically and horizontally. To the right of the sphere, a white text box with "e^(i*pi) = -1" appears to hover. A thin, golden, undulating wave-like structure emanates horizontally from the sphere, resembling a 3D sine wave. All elements have a metallic sheen, creating a symmetrical composition with a central focal point.
Prompt: (A masterpiece of unprecedented excellence), (The artwork depicts three stylized, embracing penguins lazer with vibrant patterns in bold colors. Their expressions convey a mix of emotions, emphasizing themes of connection and intimacy. By Friedensreich Hundertwasser, Transautomatism style, Figurative, Mixed media), ((As created by Joan Miró, Tomasz Setowski, Van Gogh, Picasso, Edward Gorey. Full size image)).
Prompt: Create an image of a scare crow figure sitting cross-legged among a field of pumpkins. The figure has a large, carved pumpkin for a head, featuring a playful smile and peace sign eyes. The body is adorned in vibrant, bohemian-style clothing, including an orange top with intricate patterns and flowing sleeves, The figure has long, flowing hair that is a vivid green color, decorated with a crown made of sunflowers and small wildflowers.
Surrounding the figure, there are several bright orange pumpkins scattered on the ground, with a lush field of corn in the background. The sky is a deep indigo, sprinkled with stars, and a large, luminous full moon casts a magical glow over the scene. Butterflies flutter nearby, adding to the enchanting atmosphere. The overall mood is whimsical and festive, evoking a sense of autumn magic.
Prompt: A hauntingly captivating figure, the scifi enthralling necromancer stands amidst pulsating circuitry and glowing runes, their cybernetic hands wreathed in digital flames. This mesmerizing image, a digitally painted masterpiece, exudes an otherworldly aura as the necromancer's eyes gleam with sinister intelligence. The intricate details and vivid colors in this high-quality illustration draw the viewer into a futuristic realm of dark magic and cybernetic power.
Prompt: splash ink technique aquatint, silver embossed metallic and fine intricately, detailed, black ink, lines, over the watercolor effects, picture: cartoon monster looking at viewer, full body, fantastic view, intricate, detailed, crisp quality, Colorful, tribal complementary color scheme
Prompt: A tiny, rust-colored hedgehog with delicate quills and bright, inquisitive eyes, catching a shimmering purple butterfly with intricate, swirling patterns on its wings under a canopy of twinkling fairy lights that cast a warm, soft glow, with the hedgehog's tiny paws and nose illuminated by the gentle light, and the butterfly's wings glowing with a soft, iridescent sheen, set against a backdrop of lush green foliage and vibrant, colorful flowers that add depth and texture to the scene.
Prompt: mystic Jesus, Christology Jesus Christ King of Kings, Jesus is called "King of kings" because the Bible proclaims His absolute, supreme, and ultimate authority over all earthly powers, rulers, and authorities, even those who are kings themselves. This title emphasizes His divine right to rule as the promised Messiah and the fulfillment of God's eternal kingdom, a rule that extends over all creation and will ultimately bring judgment to evil and eternal life to His people.
Prompt: Cute fluffy puppy , The style is Neo noir , sentimentalism ,elegant, Impressionism , Peter Paul Rubens , Diego Velasquez , Auguste Renoir , vintage, oil, masterpiece, high detail, art station
Prompt: A breathtakingly ultra-detailed hyperrealistic photograph captures a macabre female black cat in a ground-level shot. The feline dons an intricate black and orange outfit, complete with a witch's pointed hat adorned with a orange gemstone. Its striking yellow eyes hold a captivating gaze, while it grasps a magical staff with a glowing orange pumpkin at its tip. The cinematic, dark fantasy scene is set against a eerie pumpkinfield backdrop, with floating ghosts and ethereal lighting that further emphasize the cat's sinister and ghostly aura. The small text "@digo.a.i" is visible in the bottom right corner.
Prompt: A bold, graphic portrait of a tiger’s face, created in an abstract mosaic and stained-glass style. The design is filled with intricate hand-drawn linework, geometric shapes, and fragmented textures in orange, black, white, and turquoise tones. The eyes are vibrant and intense, framed by detailed feather-like patterns and layered organic motifs. The overall look combines animal portraiture with decorative abstract art, creating a surreal, kaleidoscopic effect.
Prompt: mystic Jesus, Christology create in the BiblicalStyle JEsus mixed with Archangel Michael the Warrior Angel with smaller Red Feathered Wings Christian theology and the clear testimony of the Bible, Jesus is not Archangel Michael. The Bible distinguishes between Jesus, who is God and worthy of worship, and angels like Michael, who are created beings and are called to worship Jesus. Passages such as Hebrews 1:5-8 and Colossians 1:16 clearly establish Jesus as superior to angels and the one through whom they were created.
Prompt: Cute fluffy puppy , The style is Neo noir , sentimentalism ,elegant, Impressionism , Peter Paul Rubens , Diego Velasquez , Auguste Renoir , vintage, oil, masterpiece, high detail, art station
Prompt: The artwork presents a sunset scene within an enchanting atmosphere, featuring elaborate floral designs and shimmering gold embellishments. The composition utilizes a mosaic patchwork backdrop with soft watercolor textures, employing a "wet on wet" technique. Inspired by Gustav Klimt's style, the piece showcases a rich color palette of gold, red, and green, aiming for an elegant and dreamy ambiance. The artwork, reflecting Gustav Klimt's artistic influence, is intended for Artstation, with a high resolution to emphasize detailed brushwork and textures.
Prompt: A surreal pink fantasy portrait in a dreamy pen-and-ink and watercolor wash style, overflowing with soft pinks, glowing highlights, and pastel tones. A whimsical, beautiful lady with exaggerated long legs and elegant stylized proportions wears bold striped stockings in black and pink, funky jewelry, and flowing whimsical clothing. She walks a fluffy pink poodle, both framed by oversized blossoms and delicate floral details. Her large, luminous eyes full of intensity and emotion are the focal point, glowing against the predominantly pink composition. The background is softly textured in watercolor shades of rose, blush, and pastel pink, blending clouds, mist, and abstract flourishes. Hyper-detailed yet dreamlike, the artwork merges whimsical fashion illustration with surreal fantasy charm — playful, sketch-like, and entirely bathed in pink vibrancy."
Prompt: cyberpunk anime woman in a white hoodie decorated with white rose embroidery and a bunny shaped gas mask with long bunny ears and golden accents. full body shot, with a cyberpunk city in the background with green lighting. graffiti is scrawled on the buildings. in the style of colored pen and ink
Prompt: A breathtaking autumnal landscape rendered in the intricate watercolor and ink style of Daniel Merriam, Ivan Shishkin, and Thomas Kincade, featuring a tranquil stone cottage with a teal roof and glowing windows nestled among vibrant flowers, greenery, and picket fences. A meandering river flows gently beneath an ancient stone bridge, surrounded by old olive trees, majestic birch trees, withered cattails, and Queen Anne's lace, set against a backdrop of mist-shrouded mountains. The soft-focus sunset sky glows with hues of Indian yellow, stark red, and earthy greens, creating an ethereal, fantastical ambiance with warm, intricate lighting. This surreal scene blends fine 3D line art and high-definition detail, capturing a harmonious retreat steeped in elegance and fantasy.
Prompt: A stunning airbrush painting captures a cozy cabin nestled in the woods at sunrise, bathed in the warm, golden glow of the rising sun. A vibrant river flows nearby, reflecting the brilliant light and adding a sense of movement to the serene scene. The highly detailed artwork showcases a radiant, glowing sun in a hot and sunny atmosphere, with fireflies dancing in the early morning air. The combination of rich colors, intricate details, and the interplay of light creates an incredible, breathtaking masterpiece that exudes warmth and beauty.
Prompt: Impasto texture painting inspired by Joan Mitchell. Abstract expressionist depiction of a solitary weathered cabin nestled beside a twisted willow on a windswept prairie, scattered with soft blooms. A moody, layered sky looms above rolling dunes at dusk, a winding brook shimmering faintly. Evokes meditative cadence, understated hues, gestural strokes, ethereal pastel tones, paint flicks, controlled chaos, graceful abstraction, and dreamlike harmony.
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.
6d
6d
