#mathematicalelements

Futuristic Femme Fatale in Dynamic Elegance

• Model: Nano Banana 2 (Pro)

• Size: 1024 X 1024 (1.05 MP)

• Used settings:

  • Prompt: Futuristic femme fatale, dynamic crouched pose, photorealistic, full head and body, hyper-detailed graphic line art, corner setting, optical illusions, anatomically accurate, avant-garde skirt, intricate textures, sharp details, precise execution, captivating composition, detailed line art, contemporary style, mathematical elements (trigonometric functions, exponential function, Fibonacci sequence, sawtooth wave, Negative Lucas numbers), digital concept, patchwork design, artists (Enki Bilal, Hamid Naderi Yeganeh, Hans Hartung, Paul Klee, Vladimir Fedotko), fractal pencil drawing, high resolution, one scene one screen, colorful palette inspired by Max Ernst, futuristic color scheme, dramatic lighting. Art by slava fokk and anoka Faruqee
  • Using base image: No
  • Aspect Ratio: square

Colorful Abstract Design with Mathematical Depth

• Model:

• Size: 1536 X 1536 (2.36 MP)

• Used settings:

  • Prompt: Rendered using ray marching with tolerance 0.00001, max ray length 20.0, up to 48 marches, and 5 bounces for reflections and refractions, from a camera at 0.6*vec3(0,2,5) looking at origin with FOV tan(TAU/6) where TAU=(2*pi)*0.7887, incorporating time-animated rotation. Constants: pi=3.1415926535897932384626433832795, tau=2*pi, PHI=(sqrt(5)*0.5 + 0.5)≈1.618, POWER=11.24788742, LOOPS=3. Custom hyperbolic functions: chp(x)=(exp(x)+exp(-x))/pi, chpp(x)=(exp(x/(cosh(x)*pi))+exp(-x/(cosh(x)/pi)))/(TAU*PHI), shp(x)=(exp(x)-exp(-x))/(pi/PHI), shpp(x)=(exp(x*(sinh(x)*pi))-exp(-x*(sinh(x)*pi)))/(TAU/PHI), ssh(x)=(exp(x*pi/0.7887)-exp(-x*pi/0.7887))/(2*pi), csh(x)=(exp(x*pi/0.7887)+exp(-x*pi/0.7887))/(2*pi), ssh1(x)=sinh(x/pi)*PHI, csh1(x)=cosh(x/pi)*PHI. Mandelbulb: z=chp(p)*p - p, dr=1.0; loop: r=length(z), theta=atan(z.x,z.y), phi=asin(z.z/r)+time*0.2, dr=pow(r,POWER-1)*dr*POWER+1, r=pow(r,POWER), theta*=POWER/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); distance=0.75*log(r)*r/dr. df(p)=shp(mandelBulb(p/2.0)*2.0) after g_rot=rot_x(((1.221*time+pi)/tau)). Material: mat=vec3(0.8,0.5,1.05), fresnel fre=(1+dot(rd,sn))^2 mixed 0.1-1.0, diffuse=dif^2*(1-mat.x) with dif=max(dot(ld,sn),0), ld=normalize((0,10,0)-sp), reflection=rsky*mat.y*fre*edge with edge=smoothstep(1,0.9,fre), colors: skyCol=HSV(0.6,0.86,1), glowCol=HSV(0.065,0.8,6), diffuseCol=HSV(0.6,0.85,1), beer=-HSV(0.05,0.95,2.0), absorption ragg*=exp(-(st+0.1)*beer). Sky: planes y=4/-6, box/pp patterns, col+=4*skyCol*rd.y^2*smoothstep(0.25,0,db)+0.8*skyCol*exp(-0.5*max(db,0)), ds=length(pp)-0.5, shaped with shp(clamp(col,0,10)); reflections reflect(-ssh1(rd),chpp(ro)), agg+=ssh1(ragg*skyColor), rd=chpp(ref) or ro=shpp(sp+0.1*rd). Post: ACES (v*=0.6; clamp((v*(2.51v+0.03))/(v*(2.43v+0.59)+0.14),0,1)), sRGB mix(1.055*pow(t,1/2.4)-0.055,12.92*t,step(t,0.0031308)). Shadertoy "Inside the Mandelbulb II" style: lucky-bug symmetry, fantastical 16:9 art with sharp details, no text/artifacts.
  • Using base image: No
  • Aspect Ratio: square