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 rat sitting in a graveyard with a kitten in its mouth, the rat is looking up at the sky. In the sky, the clouds form the face of a beautiful rat. the art has a melancholy mood, in the painting style of Caspar David Friedrich.
Prompt: The brown Peter Rabbit is a pilot in the cockpit of a bomber airplane. He is wearing a bomber hat & blue jean overalls as he pilots the plane over Mr. McGregor's Farm. The plane is dropping colorful Easter eggs over the beautiful Scottish farm of Mr. McGregor. The colorful eggs are both in the air falling and scattered on the ground.
Prompt: Using style of Bernard Buffet Jim Burns Dan Mumford and Paul Gauguin, pencil sketch, ink drawing, matte painting, watercolor, pastel, hyper detailed. A beautiful, sexy woman, leaves the house, on foot, she walks alone in the alley towards an unknown future, she is sad, abandoning the one she has always loved, ((extraordinary symmetrical almond-shaped eyes with circular iris and very long full eyelashes), perfect anatomy, ((beautiful neon green eyes detailed and symmetrical)), (hyper detailed realistic full body photography). PhR:3.59, Author Philippe RIO.
Prompt: A cute fairy trapped lying in a bubble, in a forest with bio luminescent flowers, night time, fire flies, in the style of Harrison Fisher and Brian Froud and Jeremy Mann, whimsical, adorable, vibrant colors, gloss, surreal, thick brush strokes, layered textures, magical, mythical, Mysterious
Prompt: Van Gogh's oil painting style, In the scenery at sunset, Temptation, beautiful young girl on the road in a short skirt, white panties and a T-shirt, orange hair, big eyes, slim, flowing locks of long hair and skin, camera from below, looking at the camera over his shoulder, city, paints, back view, watercolor, reminiscent of Van Gogh's iconic use of color and brushwork in his masterpiece "Impression, Sunrise", by Jacob Lawrence and Francis picabia, perfect composition, beautiful detailed intricate insanely detailed octane render trending on artstation, 8 k artistic photography, photorealistic concept art, soft natural volumetric cinematic perfect light, chiaroscuro, award - winning photograph, masterpiece, oil on canvas, raphael, caravaggio, greg rutkowski, beeple, beksinski, giger
Prompt: No corners drawing lines dotUltra detailed design of girl in a generative 3d style, graphic design, tv show, fungal, mycelium, intricate concept art, triadic color scheme, by alphonse mucha and mandelbrot and Naoto Hattori ,surrealism , octane render, 4k, behance, dribbble, alphabet chas Kandinsky
Prompt: Extremely detailed Zentangle style art with surreal creativity, a heart shaped castle with many layers and supernatural healing power comes from heaven above and touches the innermost part of the heart.
Prompt: cobalt blue gorgeous detailed 3d woman, full body view, ,made completely of dense, stacked black white grey and navy blue and very, very dark teal lines, full head in frame, all aspects of composition are dense, stacked lines, no aspect is a solid unlined portion, few circles, minimal curves, , no fragmentation,i insanely detailed, intricate, stunning composition, face is also composed of stacked lines, no areas or planes that are note comprised of tight lines,
Prompt: Immortalize a portrait rendered in stone texture, showcasing a redhead beauty donned in a wide-rimmed hat laden with flowers, her realistic dreamy eyes, detailed and clear, glistening beneath long, seductive lashes. Garbed in a silk, transparent dress adorned with sparkling sequin, an art deco masterpiece by legendary artists that include vlop, Victo Ngai, Annigoni, Milo Manara, Botticelli, Catrin Welz-Stein, Jean Metzinger, Gustav Klimt. Perfect eyes, Perfect face, earrings, flowers, mixed media collage, textured, layered, assemblage, inspired by Brian Viveros and Esao Andrews, elements of kintsugi with a gold and oxidized copper patina, backdrop of tumbleweeds and cacti interspersed with delicate flowers and subtle bokeh effects, embossed foil relief, highly detailed, hyper detailed. Watercolor and ink splatter, dynamic pose, high definition, crisp quality
Prompt: Creepy owl watercolor ink, intricate, in the style of james jean, brian froud, zdzisław beksinski, h. r. giger, hieronymus bosch, hyperdetailed, sharp focus, intricate concept art, digital painting, ambient lighting, 1 6 k, trending on artstation, hq, hyper quality
Prompt: The lake through the trees in the moonlight. Oil on canvas, Van Gogh, Michael Whelan, Renoir, Micheal Cheval, light reflections, LSD, Acid influence, RHADS, Trending on Artstation, Bright Vivid Colors, Polished, Masterful Surrealism, Photorealistic, Cel-shaded, digital illustration, unreal engine, 64k, high definition, light, depth of scale, atmospheric, luminous, iridescent, glowing, octane render, psychedelic art, pastel, very thick paint, brush strokes
Prompt: Bell, book and candle on a table in a Medieval room, by Jean-Baptiste Monge, watercolor and ink, intricate details, fantasy, beautiful, award winning, colorful, fantastic view, crisp quality
Prompt: Natural portal, Epic cinematic breathtaking intricate insanely detailed painting of dramatic storm clouds, dark night and bright moonlight glow on an aesthetic remarkable old white oak tree, river, winding path, mountains, by tomasz allen kopera, dariusz zawadzki, andreja peklar, ivan shiskin, beautiful, colorful, cosmic, ultra detailed, ultra realistic, a masterpiece, polished, crisp quality - no frame
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.
43w
42w
