Prompt: A G$_{2}$-structure on a 7-dimensional manifold is characterized by a 3-form
$\varphi $, which reduces the structure group to the exceptional Lie group
G$_{2}$. When $\varphi $ is both closed and co-closed, the structure is
torsion-free, and the associated metric is Ricci-flat. The G$_{2}$-Ricci flow is defined by the following equation
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%e3 #&#
\begin{equation}
\frac{\partial \varphi}{\partial t} = \Delta _{d} \varphi +
\mathcal{L}_{X} \varphi + \mathrm{Ric} \lrcorner \ast \varphi + T(\varphi ),
\label{eq3}
\end{equation}
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where
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\begin{itemize}
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\item $\Delta _{d}$ is the Hodge-de Rham Laplacian, a second-order elliptic
operator that acting on the 3-form $\varphi $.
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\item $\mathcal{L}_{X} \varphi $ is the Lie derivative of $\varphi $ along
a vector field $X$. It is first-order operator.
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\item $(\mathrm{Ric} \lrcorner \ast \varphi) $ is the contraction of the
Ricci tensor with the 4-form $\ast \varphi $.
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\item $T(\varphi )$ represents the torsion of the G$_{2}$-structure, which measures the deviations from the torsion-free condition.
\begin{equation}
\varphi = e^{123} + e^{145} + e^{167} + e^{246} - e^{257} - e^{347} - e^{356},
\label{eq1}
\end{equation}
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where $e^{ijk} = e^{i} \wedge e^{j} \wedge e^{k}$.
Prompt: Create an abstract digital artwork featuring an intricate tapestry of vibrant colors and patterns. The composition should consist of a swirling array of interconnected shapes, tubes, and orbs, resembling a multidimensional landscape. Incorporate a variety of spheres in diverse colors, including deep blues, bright yellows, vivid reds, and lush greens. The background should contain mystical geometric patterns, with some areas appearing mesh-like or woven. Include shiny, glossy textures in various sections, enhancing the depth and creating a sense of movement. The overall mood should evoke a sense of wonder and curiosity, inviting viewers to explore the complexities of the artwork.
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.
