Prompt:
**"Spaceship based on upon the following maths..."**: This immediately tells me you want a complex, possibly fractal-like, and intricately structured object. The "based upon maths" implies a non-organic, possibly generated or calculated appearance.
**Constants (\(\pi\), \(\text{tau}\), \(\text{PHI}\), \(\text{POWER}\), \(\text{LOOPS}\))**: These suggest a generative process, iterative refinement, and perhaps a sense of precision and complexity. The presence of PHI (the golden ratio) often hints at aesthetically pleasing, naturally occurring or fractal patterns.
**Custom hyperbolic functions (\(\text{chp}(x)\), \(\text{shp}(x)\), etc.)**: These are strong indicators of non-Euclidean geometry, curvature, twisting, and potentially organic yet structured forms. Hyperbolic functions often produce flowing, complex, and sometimes branching shapes. The specific forms like `chpp` and `shpp` with their nested hyperbolic functions and divisions by constants like `TAU/PHI` further emphasize extreme complexity and unique, perhaps alien, geometric properties.
**Mandelbulb formula (\(z=\text{chp}(p)p - p\), \(\text{dr}=1.0\); loop: \(r=\text{length}(z)\)...)**: This is the most crucial part. The Mandelbulb is a well-known 3D fractal. This directly tells me the desired image should exhibit:
**Fractal characteristics**: Self-similarity at different scales, infinite detail, recursive patterns.
**3D complexity**: The "bulb" implies a volumetric shape, not just a 2D pattern.
**Iterative generation**: The "loop" and power functions `pow(r,POWER)` describe how the fractal grows and forms its intricate surface.
**Specific transformations**: `\(\theta=\text{POWER}/\text{PHI}\)`, `\(z=r\text{vec3}(\tan(\text{shp}(\sin(\theta)\sin(\phi)))\text{PHI}, \text{chp}(\cos(\theta)\sin(\phi)), \cos(\phi))+p\)` indicate sophisticated rotations, trigonometric operations, and mapping of coordinates, which would result in highly sculptural and intertwined forms.
**Distance estimation**: `\(\text{distance}=0.75\log(r)r/\text{dr}\)` is a technique used in raymarching fractals to render surfaces, implying smooth yet incredibly detailed structures.
**Material properties (\(\text{mat}=\text{vec3}(0.8,0.5,1.05)\), \(\text{fresnel}\), \(\text{diffuse}\), \(\text{reflection}\))**: These terms describe how light interacts with the spaceship's surface.
**Specific `vec3` for `mat`**: Suggests a base color or material property.
**Fresnel**: Implies a metallic or reflective surface where reflectivity changes with the viewing angle.
**Diffuse**: Indicates some scattering of light.
**Reflection**: Explicitly states a desire for reflections, making the surface appear glossy or metallic.
**Colors (\(\text{skyCol}=\text{HSV}(0.6,0.86,1)\), \(\text{glowCol}=\text{HSV}(0.065,0.8,6)\), etc.)**: These provide a very clear color palette.
**SkyCol (blue/purple)**: Suggests a cosmic or abstract background.
**GlowCol (orange/yellow)**: Indicates emissive elements, perhaps engines or internal lighting.
**DiffuseCol (similar to skyCol)**: Reinforces the main color theme.
**Beer/Absorption**: Implies volumetric light absorption or scattering, possibly through nebulae or translucent parts of the spaceship, adding depth and atmospheric effects.
**Sky / Environment (\(y=4/-6\), box/pp patterns, `col+=4skyColrd.y^2...` )**: Describes the background and lighting.
Artist
