#scienceabstract

Fractal Harmony: Art Meets Mathematical Beauty

• Model:

• Size: 1536 X 1536 (2.36 MP)

• Used settings:

  • Prompt: > *Create a high-detail rendering inspired by the following exact mathematics. Do NOT simplify, rewrite, or omit any math. Treat all formulas, constants, and macros as aesthetic descriptors of the structure, curvature, growth rules, and lighting.* > > **Use all the following math exactly as written as the descriptive blueprint for the shapes, surfaces, distortions, rotations, color rules, and ray-marching behavior:** > > ``` > #define pi 3.1415926535897932384626433832795 > #define tau (2.*pi) > #define chp(x) (exp(x)+exp(-x))/pi > #define chpp(x) (exp(x/(cosh(x)*pi))+exp(-x/(cosh(x)/pi)))/tau*PHI > #define shp(x) (exp(x)-exp(-x))/pi > #define shpp(x) (exp(x*(sinh(x)*pi))-exp(-x*(sinh(x)*pi)))/tau*PHI > #define ssh(x) (exp(x*pi/.7887)-exp(-x*pi/.7887))/(2.*pi) > #define csh(x) (exp(x*pi/.7887)+exp(-x*pi/.7887))/(2.*pi) > #define ssh1(x) sinh(x/pi)/PHI > #define csh1(x) cosh(x/pi)/PHI > > const float POWER = 11.24788742; > const float TAU = (2.0*pi)*.7887; > const float PHI = (sqrt(5.0)*0.5 + 0.5); > > mat3 g_rot = mat3(1.0); > g_rot += outerProduct(ro, rd); > > float mandelBulb(vec3 p) { > float power = POWER; > vec3 z = chp(p)*p - p; > float dr = 1.0; > for(int i = 0; i < LOOPS; ++i) { > float r = length(z); > float theta = atan(z.x, z.y); > float phi = asin(z.z / r) + TIME*0.2; > dr = pow(r, power - 1.0) * dr * power + 1.0; > r = pow(r, power); > theta = theta * power/PHI; > phi = phi * power/PHI; > z = r * vec3(tan(shp(sin(theta)*sin(phi)))*PHI, > chp(cos(theta)*sin(phi)), > cos(phi)) + p; > p = reflect(p, z); > } > return 0.75 * (log(length(z))) * length(z) / dr; > } > > float df(vec3 p) { > p *= transpose(inverse(g_rot)); > const float z1 = 2.0; > return shp(mandelBulb(p/z1)*z1); > } > > rd = normalize(-p.x*uu + p.y*vv + tan(TAU/6.)*ww); > g_rot += outerProduct(ro, rd); > ```
  • Using base image: No
  • Aspect Ratio: square

Art Meets Science in Vibrant Abstract Sketch

• Model: FluX

• Size: 864 X 1152 (1.00 MP)

• Used settings:

  • Prompt: PUSSYART, WHISKAS CONTOUR, , DRAWING, minimalist abstract depiction of a figure with abstract body contour. Iridescent multicolor, sheen, glow, abstract brushstrokes. Elegant flowing form with gentle curves and subtle contours from head to hips, balanced and harmonious. Zen lines, serene and luminous, SCRIBBLED on a page with written MATHEMATIC CALCULATIONS
  • Using base image: No
  • Aspect Ratio: portrait

Cosmic Vibrance: Geometry of the Universe

• Model:

• Size: 1792 X 1024 (1.84 MP)

• Used settings:

  • Prompt: impact coding capability principle Interconnections energy methods explores symbolize allows principles mirrors structures existence semantics meaning showcasing programming processes mirroring operations inseparable concept cyclical function Relationships Encapsulation manifest functions Echoes
  • Using base image: No
  • Aspect Ratio: landscape