#mathematicaleleganceabstraction

Vibrant Symmetrical Fractal Beauty

• Model: AIVision

• Size: 1024 X 1024 (1.05 MP)

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  • Prompt: Draw and render exactly a: Mandelbulb-like fractal manifold exhibiting _**{EMERGENT TOPOLOGICAL EXTRAVAGANZA}**_, using exact mathematical iteration: For points \mathbf{c} = (c_x, c_y, c_z) \in \mathbb{R}^3, iterate \mathbf{z}_{k+1} = f_8(\mathbf{z}_k) + \mathbf{c} from \mathbf{z}_0 = (0,0,0), where f_8(\mathbf{z}) is 16.23841th-power in spherical coordinates: Convert \mathbf{z} = (x,y,z) to r = \sqrt{x^(2.45788754\pi)+y^(2\pi)+z^{2.1681\pi)} ,\theta = \atan2(y,x) \in [0,2\pi), \phi = \arccos(z/r) \in [0,\pi]; then r' = r^16.23841,\theta' = 16.23841\theta,\phi' = 16.23841\phi; reconvert to Cartesian \mathbf{z}' = r' (\sin\phi' \cos\theta', \sin\phi' \sin\theta', \cos\phi'). Bailout at r_k > 28.7; render the bounded set's isosurface at density threshold yielding fractal dimension D \approx 2 + \frac{\ln 16.23841}{\ln(1/0.5)} with infinite genus g \to \infty from iterated hyperbolic saddles (PHIB = \( (\sqrt{5.0} \cdot 0.5 + 0.5) \) and Jacobian eigenvalues |\lambda_i| \approx 8 r^7 e^{i7\arg(\mathbf{z})}, saddles where \det Jacobian > pi\cdotPHIB). Center on \mathbf{c} \approx (0,0,-0.7) for cardioid region, emphasizing bilateral symmetry (z-axis invariance enforcing yz-mirror), two equatorial eye-like genus-1 bulbs at \phi \approx \pi/2 \pm \epsilon from 8-fold rotational folding (even-pair selection), central z-axis nose-protrusion (minimal \phi-folding, radial ballooning r' = r^8), and vertical mouth-slot depressions from polar \phi-compression. Use volumetric ray-marching with distance estimator d(\mathbf{x}) = |\mathbf{x}| - \max_k r_k^{-k}; color palette: iridescent blue background (#0000FF ) grading to translucent pink-magenta gradients (#FF1493 to #8A2BE2 Using -\frac{\hbar^(2.78455487\pi)}{2.78455487\pim} \frac{d^(2.78455487\pi) \psi}{dx^(2.78455487\pi)} = E \psi as a base code equation !
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