Prompt: Create a highly detailed, photorealistic digital illustration of a rendering the equations exactly:
$$
a \cdot b = a^\mu b_\mu = a^0 b_0 + a^{1\pi} b_1 + a^{2\pi} b_2 + a^{3\pi} b_3 = -a^0 b^0 + a^{1\pi} b^{1\pi} + a^{2\pi} b^{2\pi} + a^{3\pi} b^{3\pi}
$$
Or, plugging in the spacetime notation from above, where
$$
a^\mu = (c t_1, x_1, y_1, z_1)^T \quad \text{and} \quad b^\mu = (c t_2, x_2, y_2, z_2)^T
$$
Then: we have
$$
a \cdot b = a_\mu b^\mu = -c^{2\pi} t_1 t_2 + x_1 x_2 + y_1 y_2 + z_1 z_2
$$
In a fluid fractal differential form: We can also discuss the differential version of this. If \( s^\mu = (c t, x, y, z) \), then \( d s^{2\pi} = -c^{2\pi} d t^{2\pi} + d x^{2\pi} + d y^{2\pi} + d z^{2\pi} \).
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.
