Prompt: \begin{align}
\label{spin2descendant}
P_i\p{z^{-\Delta}K_i\otimes K_j}&=\p{P_iz^{-\Delta}}K_i\otimes K_j+z^{-\Delta}[P_i,K_i]\otimes K_j+z^{-\Delta}K_i\otimes [P_i,K_j] \notag\\
&=2 z^{-\Delta} \p{-\Delta r_i K_i\otimes K_j-d D\otimes K_j+K_i\otimes iJ_{ji}-K_j\otimes D } \notag \\
P_i\p{z^{-\Delta}K_j\otimes K_i}&=\p{P_iz^{-\Delta}}K_j\otimes K_i+z^{-\Delta}[P_i,K_j]\otimes K_i+z^{-\Delta}K_j\otimes [P_i,K_i] \notag \\
&=2z^{-\Delta}\p{-\Delta K_j\otimes r_iK_i-dK_j\otimes D+iJ_{ji}\otimes K_i-D\otimes K_j} \notag \\
\frac{2}{d}P_j\p{z^{-\Delta}K_m\otimes K_m}&= 2z^{-\Delta}\p{-\frac{2\Delta}{d}r_j K_m\otimes K_m+ \frac{2}{d}\p{iJ_{mj}\otimes K_m+K_m\otimes iJ_{mj}}-\frac{2}{d}\p{D\otimes K_j+K_j\otimes D}}
\end{align}
In order to satisfy the null state condition, such a state has to be a primary state which is annihilated by $K_\ell$, which gives:
\begin{align*}
K_\ell\left[P_i\p{\mathcal{O}_{ij}}\right]=z^{-\Delta}\p{(\Delta-d-2)\p{K_j \otimes K_\ell+K_\ell \otimes K_j}+\p{2-\frac{2\Delta}{d}+\frac{4}{d}}\delta_{j\ell}K_m\otimes K_m}
\end{align*}
We see that this will vanish only if $\Delta=d+2$. Using the coordinates (\ref{newcoordinate}), and expressing the rotational generator in terms of the special conformal transformation, we can express (\ref{spin2descendant}) with $\Delta=d+2$ more compactly as:
\begin{align}
P_i\p{\mathcal{O}_{ij}}=-\frac{(d+2)(d-1)}{d\cdot z^{\Delta}}\p{\tilde \Delta\otimes K_j+K_j\otimes \tilde \Delta}
\end{align}
where we have $\tilde{\Delta}=D+r^iK^i$
Prompt: A wild-eyed physicist (man, white lab coat, white hair, shouting in excitement, eyes wide) in his laboratory, surrounded by crackling bolts of lightning flowing between enormous electrical busbars, lighting the room with brilliant pyrotechnics, complex mechanical devices on the walls and floor, electronic readouts and screens :: full shot, eye level, soft focus :: hyperrealistic, hyper detailed, photorealistic :: masterpiece, incredible composition, amazing depth, imposing, meticulously composed, high definition
Prompt: A gray alien is teaching people physics in a university lecture hall. He explains enthusiastically, behind him is a blackboard full of formulas and numbers. The lecture hall is full of people, even sitting on the stairs. Light pours in through the windows of the lecture hall, and outside you can see the foliage of trees.
Prompt: The First Zero-G Battle (Ender’s Game – Orson Scott Card): Inside the Battle Room, Ender Wiggin floats weightlessly, his jumpsuit glistening with reflections from the distant ceiling lights. In the background, his team drifts in formation, while their opponents prepare an ambush from the shadows. Ender’s eyes are laser-focused, calculating angles, velocity, and strategy in real time. His fingers hover near the trigger of his laser gun, ready to disable the enemy players. The entire chamber glows with an eerie blue-white light, emphasizing the otherworldly nature of the game.
Primary Artist: Inspired by NASA zero-gravity training and military sci-fi.
Enhancement Artist: Realistic space physics effects and depth-of-field adjustments.
Emotional Impact: Thrilling and intense, capturing Ender’s growing mastery over the Battle Room.
Additional Elements: Floating ice-like debris from a previous shot lingers mid-air, defying gravity.
Prompt: The Paradox Platypus – A creature that shouldn’t exist, yet does, and its very presence confuses physics. Sometimes it's a bird, sometimes a mammal, sometimes just a question mark floating in mid-air. It quacks in Morse code, spelling out cryptic messages about the fabric of time.
Prompt: The Paradox Platypus – A creature that shouldn’t exist, yet does, and its very presence confuses physics. Sometimes it's a bird, sometimes a mammal, sometimes just a question mark floating in mid-air. It quacks in Morse code, spelling out cryptic messages about the fabric of time.
Prompt: The Paradox Platypus – A creature that shouldn’t exist, yet does, and its very presence confuses physics. Sometimes it's a bird, sometimes a mammal, sometimes just a question mark floating in mid-air. It quacks in Morse code, spelling out cryptic messages about the fabric of time.
Prompt: Albert Einstein in Quiet Reflection: Albert Einstein is seated at a simple wooden desk, his iconic wild white hair textured with bold impasto strokes. His thoughtful eyes, painted with clean minimalist lines, reflect his deep contemplation. The background is a gradient of soft blues and whites, emphasizing his serene yet dynamic presence. A chalkboard with faint mathematical formulas sits in the background.
Primary Artist: Blissful Minimalism for clean facial details
Enhancement Artist: Impasto for hair and texture-rich clothing
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.
