### Deep ocean floor

Ray marching with sculpting, twisting, displacement, repetition, and sort of a fog.

// Forked from "Making waves" by PavlikEnemy
// https://turtletoy.net/turtle/13016b43d5

Canvas.setpenopacity(-0.3);

const t = new Turtle();

const scrZ = 6.0;
const scrR = 1.0;

const eyeZ = 9.0;

const camRotX = -60 * Math.PI/180;
const camRotY = -15 * Math.PI/180;

const step = 0.25;

const Dmax = scrZ + 120;

const EPS = 0.0001;

const MAX_N_STEPS = 256;

function plus(v1, v2) {
return [v1[0] + v2[0], v1[1] + v2[1], v1[2] + v2[2]];
}

function minus(v1, v2) {
return [v1[0] - v2[0], v1[1] - v2[1], v1[2] - v2[2]];
}

function mod(v1, v2) {
return [v1[0] % v2[0], v1[1] % v2[1], v1[2] % v2[2]];
}

function multiply(a, v) {
return [a * v[0], a * v[1], a * v[2]];
}

function abs(v) {
return [Math.abs(v[0]), Math.abs(v[1]), Math.abs(v[2])];
}

function length(v) {
return Math.sqrt(v[0]**2 + v[1]**2 + v[2]**2);
}

function normalize(v) {
return multiply(1 / length(v), v);
}

function rotate(v, phi) {
return [v[0] * Math.cos(phi) - v[1] * Math.sin(phi),
v[0] * Math.sin(phi) + v[1] * Math.cos(phi)];
}

function cast_ray_from_screen(x, y) {
let px = -scrR + 2 * scrR * (x / 200);
let py = -scrR + 2 * scrR * (y / 200);
let pz = scrZ;

[px, py] = rotate([px, py], camRotY);
[py, pz] = rotate([py, pz], camRotX);

let ex = 0, ey = 0, ez = eyeZ;

//[ex, ey] = rotate([ex, ey], camRotY)
[ey, ez] = rotate([ey, ez], camRotX)

let p = [px, py, pz];
let eye = [ex, ey, ez];

let dir = normalize(minus(p, eye));

return [p, dir];
}

function intersect_df(p, dir, df) {
let D = 0;
var n_steps;

for (n_steps = 0; n_steps < MAX_N_STEPS; n_steps++) {
let d = scene_df(p);

if ((d < EPS) || (D > Dmax)) {
break;
}
else {
p = plus(p, multiply(d, dir));

D += d;
}
}

return [p, D, n_steps];
}

function cylinder_df(p, c, h, r) { // axis z
const [px, py, pz] = minus(p, c);

let dxy = Math.sqrt(px**2 + py**2) - r;
let dz = Math.abs(pz) - h/2;

if (dxy > 0) {
if (dz > 0) {
return Math.sqrt(dxy**2 + dz**2);
}
else {
return dxy;
}
}
else {
if (dz > 0) {
return dz;
}
else {
return Math.max(dxy, dz);
}
}
}

function plane_df(p) { // z = 0
return p[2];
}

function sphere_df(p, c, r) {
return length(minus(c, p)) - r;
}

// see https://iquilezles.org/articles/smin/
function smooth_min(a, b, k) {
let h = Math.max(k - Math.abs(a - b), 0) / k;
return Math.min(a, b) - h*h*h*k*(1/6);
}

function smooth_max(a, b, k) {
return -smooth_min(-a, -b, k);
}

function scene_df(p) {
const r = 0.075;
const h = 2.5;

p0 = p;

const periods = [1.0, 1.5, 100.0];
const half_periods = multiply(0.5, periods);

let hx = Math.floor((Math.abs(p[0]) + periods[0]/2) / periods[0]);
let hy = Math.floor((Math.abs(p[1]) + periods[1]/2) / periods[1]);
let hash = 1 - 2 * ((Math.sin(hx * 12.9898 + hy * 78.233) * 43758.5453) % 1);

//let phi = p[2] * 5 - Math.PI/2;
let phi = p[2] * 5 - 2 * Math.PI * hash;

p = plus(p, [101, 99, 0]);
p = minus(mod(plus(p, half_periods), periods), half_periods);

let [px, py] = rotate([p[0], p[1]], phi);

let p_tr = [px, py, p[2]];

let c = [0, 0.1, 0];
let cyl_df = cylinder_df(p_tr, c, h, r);

let cr1 = 2 * r;
let cs1 = [c[0], c[1], c[2] + h/2];
let sph1_df = sphere_df(p_tr, cs1, cr1);

let cr3 = 1.25 * r;
let a = 1.25;
let dr = 1.5 * cr1;
let cs3 = [c[0] - dr, c[1], c[2] + h/2 + a * cr1];
let sph3_df = sphere_df(p_tr, cs3, cr3);
cs3 = [c[0] + dr, c[1], c[2] + h/2 + a * cr1];
sph3_df = Math.min(sph3_df, sphere_df(p_tr, cs3, cr3));
cs3 = [c[0], c[1] - dr, c[2] + h/2 + a * cr1];
sph3_df = Math.min(sph3_df, sphere_df(p_tr, cs3, cr3));
cs3 = [c[0], c[1] + dr, c[2] + h/2 + a * cr1];
sph3_df = Math.min(sph3_df, sphere_df(p_tr, cs3, cr3));

let cr2 = 2.0 * r;
let cs2 = [c[0], c[1], c[2] + h/2 + cr1];
let sph2_df = sphere_df(p_tr, cs2, cr2);

let pl_df = plane_df(p);

let noise1 = 0.015 * Math.sin(30 * p_tr[0]) * Math.sin(30 * p_tr[1]) * Math.sin(40 * p_tr[2]);
//let noise2 = 0.025 * Math.sin(31 * (p0[0] + 2 * p0[1])) * Math.sin(29 * (p0[1])) * Math.sin(40 * p0[2]);

var df;
df = smooth_min(cyl_df, sph1_df, 0.05);
df = smooth_min(df, sph3_df, 0.3);
df = smooth_max(df, -sph2_df, 0.05);
df += noise1
//pl_df += noise2
//pl_df += 0.005 * (1 - 2 * ((Math.sin(10*p0[0] * 12.9898 + 10*p0[1] * 78.233) * 43758.5453) % 1))
pl_df += 0.2 * (1 - 2 * ((Math.sin(10*p0[0] * 12.9898 + 10*p0[1] * 78.233) * 43758.5453) % 1))
df = smooth_min(pl_df, df, 0.75);
//df += 0.005 * (1 - 2 * ((Math.sin(10*p0[0] * 12.9898 + 10*p0[1] * 78.233) * 43758.5453) % 1))
//df += 0.002 * (1 - 2 * ((Math.sin(10*p0[0] * 12.9898 + 10*p0[1] * 78.233) * 43758.5453) % 1))

return df;
}

let x = 0;
let y = 0;

function walk(frame) {
const [p, dir] = cast_ray_from_screen(x, y);

const [p_int, dist_to_int, n_steps] = intersect_df(p, dir, scene_df);

if (dist_to_int < Dmax) {
let s = step * Math.max(0.1, (1 - n_steps / 50))**2.5;

t.seth(360 * Math.random());

for (let i = 0; i < 4; i++) {
t.jump(x - 100, y - 100);
t.right(90);
t.forward(s);
}
}

x += step;
if (x > 200) {
y += step;
x = 0;
}

return (y < 200);
}