Intricate Metallic Organic Fractal Lattice

Intricate Metallic Organic Fractal Lattice

• Model: Ideogram v4 (Pro)

• Size: 3840 X 2160 (8.29 MP)

• Used settings:

  • Prompt: Render a 16:9 wide-angle 3D raymarched scene of a bounded, porous gyroid network viewed from inside the struts, matching a raw single-sample-per-pixel GPU shader with aliased silhouettes and blown-out linear lighting. **1. Camera & Ray Generation ($\theta \approx 90^\circ$):** $$\mathbf{r}(t) = \mathbf{o} + t\,\hat{\mathbf{d}}, \quad \hat{\mathbf{d}} = \operatorname{normalize}\!\left(a\tan\!\left(\frac{\theta}{2}\right)x_{\text{ndc}}\,\hat{\mathbf{u}} + \tan\!\left(\frac{\theta}{2}\right)y_{\text{ndc}}\,\hat{\mathbf{v}} + \hat{\mathbf{w}}\right)$$ **2. Bounded Gyroid Implicit Surface ($c \in (0.3, 0.8)$):** $$G(\mathbf{p}) = \sin(kx)\cos(ky) + \sin(ky)\cos(kz) + \sin(kz)\cos(kx)$$ $$f(\mathbf{p}) = \max\!\Big(\alpha\big(G(\mathbf{p}) - c\big),\; \|\mathbf{p}\|_q - R\Big)$$ *(1–2 layers of thick, twisting 3-way tubular struts opening onto a flat slate-blue void $\mathbf{C}_{\text{sky}} = (0.38, 0.47, 0.56)$.)* **3. Sphere Tracing & Normals:** $$t_{n+1} = t_n + \frac{s \cdot f(\mathbf{r}(t_n))}{\lambda}, \quad \hat{\mathbf{n}} = \frac{\nabla G(\mathbf{p})}{\|\nabla G(\mathbf{p})\|}$$ $$\nabla G(\mathbf{p}) = k \begin{pmatrix} \cos(kx)\cos(ky) - \sin(kz)\sin(kx) \\ \cos(ky)\cos(kz) - \sin(kx)\sin(ky) \\ \cos(kz)\cos(kx) - \sin(ky)\sin(kz) \end{pmatrix}$$ *(Terminate on $|f(\mathbf{r}(t_n))| < \epsilon$ or escape to $\mathbf{C}_{\text{sky}}$ when $t_n > t_{\max}$; single sample per pixel, crisp un-antialiased edges.)* **4. Albedo Texture (Striated Bark & Concentric Knots):** $$u(\mathbf{p}) = \operatorname{fract}\!\left(\beta\,\|\mathbf{p}_{xy}\| + \gamma\sum_{i=0}^{M-1} 2^{-i}\,\operatorname{noise}\!\left(2^i\mathbf{p}\right)\right)$$ *(Map $u(\mathbf{p})$ or triplanar weights $w_i = |\hat{n}_i|^p / \sum_j |\hat{n}_j|^p$ to pale pink, cream, olive-yellow, and dark mottled brown bark textures with concentric ring contours around extrema.)* **5. Clamped Linear Lighting (Overexposed, No Tone Mapping):** $$\mathbf{C}_{\text{final}} = \operatorname{clamp}\!\Big(\mathbf{C}_{\text{albedo}} \odot \big(\mathbf{I}_a + \mathbf{I}_l\max(0, \hat{\mathbf{n}}\cdot\hat{\mathbf{l}})\big) + \mathbf{I}_s\max(0, \hat{\mathbf{n}}\cdot\hat{\mathbf{h}})^m,\; 0,\; 1\Big)$$ *(Use $\|\mathbf{I}_l\| > 1$ so lit ridges clip to pure white and pale yellow while shadowed undersides remain dark speckled brown.)*
  • Using base image: No
  • Aspect Ratio: landscape_wide