// Computes f(x,y,z). You may use x2 for x*x, x3 for x*x*x, // same holds for y and z. Constant must be floating numbers. // Durckblick + ball return ( x2 + y2 + z2 - a*a ) * ( x3 * y + x * z3 + y3 * z + 5. * z ); { "name" : "Durchball", "frag" : "durchball", "display_mode" : [ 0, 2, 5, 6, 7 ], "color_model" : [ 1, 2 ], "a" : [1.0, 1.5], "scale" : [15.0, 20.0], "iso" : [-0.8, 0.8], "grid_size" : [0.3, 0.4 ], "grid_thickness" : [0.0, 0.1 ], "curv_scale" : [1.0, 2.0 ], "princ_curv" : [0,2] } // Crixxi float d = y2 + z2 - a*a; float e = x2 + y2 - a*a; return 0.9*d*d + e*e*e; { "name" : "Crixxi", "frag" : "crixxi", "display_mode" : [ 0, 2, 4, 6 ], "color_model" : [ 1, 2 ], "a" : [ 1.0, 1.0], "scale" : [30.0,30.0], "iso" : [-0.005, 0.005], "curv_scale" : [2.5, 2.5], "grid_size" : [0.1, 1.0], "grid_thickness" : [0.0, 0.2], "view_shape" : [4] } // CayleyCubic return x2 + y2 + z2 + x2*z - y2*z - 1.; { "name" : "Cayley cubic", "frag" : "cayleycubic", "display_mode" : [ 0, 1, 6 ], "color_model" : [ 1, 2 ], "scale" : [10.0, 20.0], "iso" : [-0.1, 0.1], "grid_size" : [0.1, 1.0 ], "grid_thickness" : [0.0, 0.1 ], "view_shape" : [4] } // Durchblick return x3 * y + x * z3 + y3 * z + a*z3 + 5. * z; { "name" : "Durchblick", "frag" : "durchblick", "display_mode" : [ 2, 3, 5, 6, 7 ], "color_model" : [ 1, 2 ], "a" : [1.0, 1.5], "scale" : [15.0, 20.0], "iso" : [-0.1, 0.1], "grid_size" : [0.4, 0.5 ], "grid_thickness" : [0.1, 0.1 ], "princ_curv" : [0,1,2], "curv_scale" : [1.0,1.0], "view_shape" : [4] } // BarthSextic float x4 = x2*x2; float y4 = y2*y2; float z4 = z2*z2; return z4*z2 + 5.*(x2+y2)*(-z4 + (x2+y2)*z2) - 2.*(x4 - 10.*x2*y2+5.*y4)*x*z + 1.25*pow(a*(x2+y2+z2-a*a),2.0); { "name" : "Barth sextic", "frag" : "barthsextic", "display_mode" : [ 0, 1, 2, 6, 7 ], "color_model" : [ 0, 1 ], "a" : [1.0, 1.0], "scale" : [10.0, 20.0], "iso" : [-0.2, 0.2], "grid_size" : [0.0, 0.0 ], "grid_thickness" : [0.0, 0.0 ], "view_shape" : [4] } // ClebschDCubic float d = x + y + z + a; return x3 + y3 + z3 + a*a*a - d*d*d; { "name" : "Clebsch diag. cubic", "frag" : "clebschdcubic", "display_mode" : [ 0, 1, 5, 6 ], "color_model" : [ 0, 1, 2 ], "a" : [1.0, 1.0], "scale" : [20.0, 30.0], "iso" : [-0.2, 0.2], "grid_size" : [0.35, 0.4 ], "grid_thickness" : [0.0, 0.1 ] } // BohemianDome float d = x2 + y2 + z2 - a*a - b*b; return d*d - 4.*(a*a - x2)*(b*b - y2); { "name" : "Bohemian dome", "frag" : "bohemiandome", "display_mode" : [ 0, 2, 3, 4, 6, 7 ], "color_model" : [ 1, 2 ], "a" : [0.8, 1.2], "b" : [0.8, 1.2], "scale" : [20.0, 23.0], "iso" : [-0.1, 0.1], "curv_scale" : [3.0, 3.0], "grid_size" : [0.0, 0.0 ], "grid_thickness" : [0.0, 0.0 ] } // Gyroid return a*cos(x)*sin(y)+b*cos(y)*sin(z)+c*cos(z)*sin(x); { "name" : "Gyroid", "frag" : "gyroid", "display_mode" : [ 0, 2, 3, 4, 5 ], "color_model" : [ 1, 2 ], "a" : [0.5, 1.5], "b" : [0.5, 1.5], "c" : [0.5, 1.5], "scale" : [14.0, 18.0], "iso" : [0.0, 0.0], "curv_scale" : [0.15, 0.15], "princ_curv" : [0,1,2], "grid_size" : [0.35, 0.4 ], "grid_thickness" : [0.0, 0.1 ] } // Neovius return 3.*a*(cos(x) + cos(y) + cos(z)) + 4.*b*cos(x)*cos(y)*cos(z); { "name" : "Neovius", "frag" : "neovius", "display_mode" : [ 0, 2, 3, 4, 5 ], "color_model" : [ 1, 2 ], "a" : [0.5, 1.5], "b" : [0.5, 1.5], "scale" : [6.0, 15.0], "iso" : [-1.0, 1.0], "curv_scale" : [1.0, 1.0], "grid_size" : [0.1, 1.0 ], "grid_thickness" : [0.0, 0.1 ] } // KleinBottle (Ian Stewart) float l2 = a*(x2+y2+z2); float w = l2 - 2.0*y - b; return (l2 + 2.0*y - b)*(w*w - 8.0*z2) + 16.0*x*z*w; { "name" : "Klein bottle", "frag" : "kleinbottle", "display_mode" : [ 5, 6, 7 ], "color_model" : [ 1, 2 ], "a" : [1.0, 1.0], "scale" : [10.0, 13.0], "iso" : [-0.1, 0.1], "grid_size" : [0.25, 0.25 ], "grid_thickness" : [0.4, 0.5 ], "princ_curv" : [1,2], "view_shape" : [4] } // PluckerConoid return z*pow( x2+y2, 2.5 ) - (x3*x2 - 10.0*x3*y2 + 5.0*x*y2*y2); { "name" : "Plucker conoid", "frag" : "pluckerconoid", "display_mode" : [ 0, 2, 3, 4, 5, 6, 7 ], "color_model" : [ 1, 2 ], "a" : [1.0, 1.0], "scale" : [15.0, 15.0], "iso" : [-0.01, 0.01], "grid_size" : [0.5, 0.5 ], "grid_thickness" : [0.1, 0.1 ], "princ_curv" : [0,1,2], "curv_scale" : [0.25,0.25], "view_shape" : [4] } // Ellipsoid return (x2/(a*a)+y2/(b*b)+z2/(c*c)-1.); { "name" : "Ellipsoid", "frag" : "ellipsoid", "display_mode" : [ 5 ], "color_model" : [ 0, 1 ], "scale" : [24.0, 24.0], "iso" : [0.0, 0.0], "a" : [2.0, 2.0], "b" : [1.5, 1.5], "c" : [1.0, 1.0], "grid_size" : [0.2,0.3], "princ_curv": [0,1,2], "curv_scale": [1.0,1.0] } // Torus return (x2+y2+z2+a*a-b*b)*(x2+y2+z2+a*a-b*b)-4.*a*a*(x2+y2); { "name" : "Torus", "frag" : "torus", "display_mode" : [ 2, 3, 5, 6, 7 ], "color_model" : [ 1, 2 ], "scale" : [10.0, 12.5], "iso" : [0.0, 0.0], "a" : [1.75, 2.0], "b" : [1.0, 1.5], "princ_curv" : [0], "grid_size" : [0.2,0.3], "center_x" : [0.3,0.3], "center_y" : [0.1,0.2], "center_z" : [-0.1,0.1], "curv_scale" : [0.25,0.25], "view_shape" : [4] } // Cubes in infinite directions float d = 0.5*a*b; return -0.25 + max( abs( mod( p.x, a ) - d ), max( abs( mod( p.y, a ) - d ), abs( mod( p.z, a ) - d ) ) ); { "name" : "Infinite cubes", "frag" : "infinite-cubes", "display_mode" : [ 0, 1 ], "color_model" : [ 1, 2 ], "scale" : [5.0, 15.0], "iso" : [0.0, 0.0], "a" : [1.0, 1.0], "b" : [0.2, 1.8], "view_shape" : [0] } // Kleinian variation (taken from shadertoy (Spudsville2018, by EvilRyu) const int depth = 8; //< depth of the fractal ! Increase at your own risk... vec3 d = vec3( a, b, c ); //< Try (1,0.225,1.15) float scale = 1.0; for( int i = 0; i < depth; i++) { p = 2.0*clamp(p, -d, d) - p; float r2 = dot(p,p); float k = max((1.)/(r2), 0.03); p *= k; scale *= k; } float l = length(p.xy); float rxy = l - 3.; float n = l * p.z; rxy = max(rxy, -(n) / (length(p))-0.02); return (rxy) / abs(scale) + 0.0001; //thicken a little bit { "name" : "Kleinian variation", "frag" : "kleinian", "display_mode" : [ 0, 2 ], "color_model" : [ 1 ], "scale" : [10.0, 35.0], "iso" : [0.0, 0.0], "abc" : [ [0.475, 0.425, 1.15], [1.0, 0.2, 1.25] ], "curv_scale" : [50.0, 50.0], "grid_thickness" : [0.0, 0.0 ] } // Kind of virus const vec3 xc = vec3(0.,0.,0.); vec3 d = vec3(x,y,z) - xc; vec3 n = normalize( d ); vec2 theta = normalize (d.xy); float dd = length( n.xy ); float tt = atan( theta.y, theta.x ); float phi = atan( n.z, dd ); const float nbu = 22.; const float nbv = 26.; float u = pow(cos( tt * nbu ), 9.0); float v = pow(cos( phi * nbv ), 9.0); float d2 = dot(d,d); return d2-a*a - 0.2*u*v/(1.+1.*d2); { "name" : "Virus", "frag" : "virus", "display_mode" : [ 0, 6 ], "color_model" : [ 1, 2 ], "a" : [1.0,1.0], "b" : [1.0,1.0], "c" : [1.0,1.0], "scale" : [30.0,35.0], "iso" : [-1.0, 1.0], "view_shape" : [4] } // Whitney umbrella return x2 - y2*z; { "name" : "Whitney umbrella", "frag" : "whitney-umbrella", "display_mode" : [ 0, 6, 7 ], "color_model" : [ 1, 2 ], "scale" : [10.0,20.0], "iso" : [0.0, 0.01] } // Sierpinski's cube / fractal const int n = 4; // depth of Sierpinski's cube (increase for less volume) float l = 3.0 * a; float d = max( max( x - l, -l - x ), max( max( y - l, -l - y ), max( z - l, -l - z ) ) ); vec3 c = vec3( 0., 0., 0. ); for ( int i = 0; i < n && d < 0.; i++ ) { l /= 3.0; float dx = abs(x - c.x); float dy = abs(y - c.y); float dz = abs(z - c.z); float ax = max( dy, dz ); float ay = max( dx, dz ); float az = max( dx, dy ); float dp = min( ax, min( ay, az ) ); float nd = l - dp; d = max( d, nd ); float ll = 2.0*l; c.x += ll*round( (x - c.x) / ll ); c.y += ll*round( (y - c.y) / ll ); c.z += ll*round( (z - c.z) / ll ); } return d; { "name" : "Sierpinski's cube", "frag" : "sierpinski-cube", "display_mode" : [ 0, 6 ], "color_model" : [ 1 ], "scale" : [10.0, 10.0], "accuracy" : 2.0, "iso" : [0.0, 0.0] } // Goursat surface (quartic) with tetrahedral symmetry. return (x+y+z-a)*(-x-y+z-a)*(x-y-z-a)*(-x+y-z-a)+b*(x2+y2+z2-3.*a)*(x2+y2+z2-3.*a); { "name" : "Goursat tetra", "frag" : "goursat-tetra", "display_mode" : [ 0, 1, 2, 5, 6 ], "color_model" : [ 1, 2 ], "scale" : [10.0,14.0], "a" : [0.5,1.0], "b" : [0.5,1.0], "iso" : [-0.1, 0.1], "curv_scale" : [1.0, 1.0], "grid_size" : [0.05, 0.5 ], "grid_thickness" : [0.1, 0.1 ] } // Goursat surface (quartic) with octahedral/cube symmetry. return x2*x2+y2*y2+z2*z2+a*(x2+y2+z2)*(x2+y2+z2)+b*(x2+y2+z2)+c; { "name" : "Goursat octa", "frag" : "goursat-octa", "display_mode" : [ 0, 1, 2, 5, 6 ], "color_model" : [ 1, 2 ], "scale" : [15.0,20.0], "abc" : [ [0.0,-1.0,0.0], [-1.0,-0.25,0.25], [-1.0,1.0,1.0], [0.0,-2.0,2.0], [-1.0,4.0,6.0], [-0.5,-1.0,0.5], [-0.075, -1.5, 1.3] ], "iso" : [-0.01, 0.01], "curv_scale" : [3.0, 3.0], "grid_thickness" : [0.1, 0.1 ], "grid_size" : [0.25, 0.35 ], "princ_curv" : [0,1,2] } // Julia set const int n = 30; //< max iterations float cx = a; float cy = b; float zx = y; float zy = z; int i = 0; for ( i = 0; i < n; i++ ){ vec2 nz = vec2( zx*zx - zy*zy + cx, 2.0*zx*zy + cy ); zx = nz.x; zy = nz.y; // we know that the series is divergent when |z| > 2.0 if ( dot(nz,nz) > 4.0 ) break; } return(2.0/(zx*zx+zy*zy)*float(i)/29.0) - 1.*(1.0-10.1*abs(x)); { "name" : "Julia set", "frag" : "julia", "display_mode" : [ 0 ], "color_model" : [ 1 ], "a" : [-0.5, 0.5], "b" : [-0.5, 0.5], "scale" : [33.0, 40.0], "iso" : [0.0, 0.0], "view_shape" : [ 4,7 ], "animate_a" : [ 4.0, 0.3 ], "animate_b" : [ 2.0, 0.2 ] } // Beating heart const float amp = 0.2; float ft = -abs(cos(6.*t)); float ax = z*(1.+amp*ft); float ay = x*(1.+amp*ft); float az = y*(1.+amp*ft); float ax2 = ax*ax; float ax3 = ax*ax2; float ay2 = ay*ay; float ay3 = ay*ay2; float az2 = az*az; float az3 = az*az2; float w = ax2+9./4.*ay2+az2-1.; return (w*w*w - ax2*az3 - 9./80.*ay2*az3); { "name" : "Beating heart", "frag" : "beating-heart", "display_mode" : [ 0, 2, 6 ], "color_model" : [ 1 ], "scale" : [25.0, 25.0], "iso" : [0.0, 0.0], "view_shape" : [ 4 ], "grid_size" : [1.0,1.0], "grid_thickness" : [0.0,0.0], "singularity" : 0.0 }