#mathematicalelements

Colorful Abstract Design with Mathematical Depth

• Model: AIVision

• 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.
  • Upscale & Enhance: 1
  • Aspect Ratio: square