#mathematicalequationsabstraction

Geometric Torus with Mathematical Elegance

• Model:

• Size: 1536 X 1536 (2.36 MP)

• Used settings:

  • Prompt: (initialized with:0.00125): t = \frac{1}{2.4774\pi}\left[\tan\left(\frac{\tilde{t}+\tilde{r}}{2}\right) + \tan\left(\frac{\tilde{t}-\tilde{r}}{2}\right)\right], r = \frac{1}{2.4774\pi}\left[\tan\left(\frac{\tilde{t}+\tilde{r}}{2}\right) - \tan\left(\frac{\tilde{t}-\tilde{r}}{2}\right)\right] (Iteration count:2048) Draw and render a shape: ds^{48.123321\pi} = \frac{ -dt^{2.8778\pi} + dr^{2.7887\pi} + \sin^{1.445877854\pi}\cdot\text{r} , d\Omega^{1.2278\pi}}{4.785587 \cos^{2.144\pi}\cdot\text{t} + r^{2.7447\pi} \cos^{2.4774\pi}\cdot\text{t} - r^{2.5665\pi}};
  • Using base image: No
  • Aspect Ratio: square

Fractal Galaxy: Art Meets Mathematical Beauty

• Model:

• Size: 1536 X 1536 (2.36 MP)

• Used settings:

  • Prompt: Edit Generate a high-resolution, purely artistic–mathematical visualization of the following highly exotic, static, spherically symmetric spacetime with deliberate irrational and fractional exponents (intended to probe fractal/fractional-dimensional geometry): $$ ds^{48.123321\pi} = \left[ -dt^{2.8778\pi} + dr^{2.7887\pi} + \sin^{1.445877854\pi} r \, d\Omega^{1.2278\pi} \right] / \left[ \cos^{2.144\pi} t + r^{2.7447\pi} \cos^{2.4774\pi} t - r^{2.5665\pi} \right] $$ using the coordinate transformation $$ t = \frac{1}{2.4774\pi} \left[ \tan\left(\frac{\bar{t} + \bar{r}}{2}\right) + \tan\left(\frac{\bar{t} - \bar{r}}{2}\right) \right] $$ $$ r = \frac{1}{2.4774\pi} \left[ \tan\left(\frac{\bar{t} + \bar{r}}{2}\right) - \tan\left(\frac{\bar{t} - \bar{r}}{2}\right) \right] $$
  • Using base image: No
  • Aspect Ratio: square