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hyperrogue/rogueviz/collatz.cpp

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#include "rogueviz.h"
namespace rogueviz {
namespace collatz {
double s2, s3, p2, p3;
double cshift = -1;
transmatrix T2, T3;
edgetype *collatz1, *collatz2;
void act(vertexdata& vd, cell *c, shmup::monster *m, int i);
void lookup(long long reached, int bits);
void collatz_video(const string &fname);
void start() {
init(RV_GRAPH);
collatz1 = add_edgetype("1");
collatz2 = add_edgetype("2");
vdata.resize(1);
vertexdata& vd = vdata[0];
createViz(0, cwt.at, xpush(cshift));
virtualRebase(vd.m);
vd.cp = dftcolor;
vd.data = 0;
addedge(0, 0, 1, false, collatz::collatz1);
vd.name = "1";
storeall();
T2 = spin(collatz::s2) * xpush(collatz::p2);
T3 = spin(collatz::s3) * xpush(collatz::p3);
rv_hook(hooks_drawvertex, 100, act);
rv_hook(hooks_args, 100, [] {
using namespace arg;
if(0) ;
#if CAP_SHOT
else if(argis("-rvvideo")) {
shift(); collatz_video(arg::args());
}
#endif
else if(argis("-collatz-go")) {
shift(); int i = argi(); shift(); int j = argi();
if(i <= 0) i = 763;
if(j < 0 || j > 61) j = 61;
collatz::lookup(i, j);
}
else return 1;
return 0;
});
}
void lookup(long long reached, int bits) {
while(reached < (1ll<<bits)) {
if(reached%3 == 2 && (2*reached-1) % 9 && hrand(100) < 50)
reached = (2*reached-1) / 3;
else reached *= 2;
}
println(hlog, "reached = ", llts(reached));
vector<string> seq;
while(reached>1) {
seq.push_back(llts(reached));
if(reached&1) reached += (reached>>1)+1;
else reached >>= 1;
}
// seq.push_back("1");
reverse(seq.begin(), seq.end());
int id = 0;
int next = 0;
int steps = 0;
while(true) {
steps++;
if(std::isnan(View[0][0])) exit(1);
shmup::turn(100);
drawthemap();
centerpc(100); optimizeview();
fixmatrix(View);
bfs(); setdist(cwt.at, 7 - getDistLimit() - genrange_bonus, NULL);
vertexdata& vd = vdata[id];
for(int e=0; e<isize(vd.edges); e++) {
int id2 = vd.edges[e].first;
if(vdata[id2].name == seq[next]) {
id = id2; next++;
cwt.at = vdata[id2].m->base;
if(shmup::on) shmup::pc[0]->base = cwt.at;
if(next == isize(seq)) goto found;
}
}
}
found:
printf("steps = %d\n", steps);
}
void act(vertexdata& vd, cell *c, shmup::monster *m, int i) {
if(c->cpdist > 7 && euclid) ;
else if(vd.data == 2) {
// doubler vertex
string s = vd.name;
colorpair cp = vd.cp;
vd.data = 20;
int i0 = isize(vdata);
vdata.resize(i0+1);
vertexdata& vdn = vdata[i0];
createViz(i0, m->base, m->at * collatz::T2);
virtualRebase(vdn.m);
vdn.cp = perturb(cp);
vdn.data = 0;
addedge(i, i0, 1, false, collatz::collatz1);
vdn.m->store();
int carry = 0;
string s2 = s;
for(int i=isize(s2)-1; i>=0; i--) {
int x = 2*(s2[i] - '0') + carry;
carry = x>=10;
if(carry) x-=10;
s2[i] = '0'+x;
}
if(carry) s2 = "1" + s2;
vdn.name = s2;
int m3 = 0;
for(int i=0; i<isize(s); i++) m3 += s[i] - '0';
if(m3 % 3 == 2 && s != "2" && s != "1") {
vdata.resize(i0+2);
vertexdata& vdn = vdata[i0+1];
createViz(i0+1, m->base, m->at * collatz::T3);
virtualRebase(vdn.m);
vdn.cp = perturb(cp);
vdn.data = 0;
addedge(i, i0+1, 1, false, collatz::collatz2);
vdn.m->store();
int carry = -1;
string s2 = s;
for(int i=isize(s2)-1; i>=0; i--) {
carry += 2 * (s2[i] - '0');
int ncarry = 0;
while(carry % 3) carry += 10, ncarry--;
if(carry >= 30) carry -= 30, ncarry += 3;
s2[i] = '0'+carry/3;
carry = ncarry;
}
if(s2[0] == '0') s2 = s2.substr(1);
vdn.name = s2;
vdn.cp = perturb(vdn.cp);
}
}
else if(vd.data < 2) {
vd.data++;
fixmatrix(vd.m->at);
}
}
#if CAP_SHOT
// see: https://www.youtube.com/watch?v=4Vu3F95jpQ4&t=6s (Collatz)
void collatz_video(const string &fname) {
if(true) {
sightrange_bonus = 3;
genrange_bonus = 3;
dronemode = true; pconf.camera_angle = -45; rog3 = true; patterns::whichShape = '8';
vid.aurastr = 512;
collatz::lookup(763, 60);
history::create_playerpath(), models::rotation = 1;
// pmodel = mdBand;
#define STORYCOUNT 24
#define T(m,ss) (60*24*(m)+24*(ss))
#define FRAMECOUNT T(4,55)
printf("framecount = %d\n", FRAMECOUNT);
struct storydata { int s; int e; const char *text; } story[] = {
{T(0,14), T(0,17), "I am flying above a tree of numbers."},
{T(0,17), T(0,20), "It starts with the number 1."},
{T(0,20), T(0,23), "Each number n branches left to 2n."},
{T(0,23), T(0,28), "And it branches right to (2n-1)/3 if possible."},
{T(1, 8), T(1,11), "What I am flying above is not a plane."},
{T(1,11), T(1,14), "It is not a sphere either."},
{T(1,14), T(1,17), "To be honest, the space I live in..."},
{T(1,17), T(1,20), "...is not even Euclidean."},
{T(2,12), T(2,15), "Look, angles of a triangle add up to..."},
{T(2,15), T(2,18), "...less than 180 degrees in this world."},
{T(2,18), T(2,21), "6/7 of 180 degrees, to be exact."},
{T(2,21), T(2,24), "Do you see the regular heptagons?"},
{T(2,36), T(2,42), "And all these lines are straight."},
{T(3, 8), T(3,11), "Lots of space in my world."},
{T(3,11), T(3,14), "In 105 steps from the root..."},
{T(3,14), T(3,17), "...there are trillions of numbers."},
{T(3,17), T(3,20), "That would not fit in your world."},
{T(4,0), T(4,3), "Is every positive number somewhere in the tree?"},
{T(4,3), T(4,6), "Your mathematicians do not know this yet."},
{T(4,6), T(4,10), "Will you find the answer?"},
{T(4,44), T(4,54), "music: Ambient Flow, by Indjenuity"},
{T(2,6), T(2,27), "@triangles"},
{T(2,27), T(2,42), "@network"},
{0, T(0,7), "@fi"},
{T(4,48), T(4,55), "@fo"},
{0,0,NULL}
};
int drawtris=0, drawnet=0;
for(int i=0; i<FRAMECOUNT; i++) {
const char *caption = NULL;
int fade = 255;
bool dt = false, dn = false;
for(int j=0; story[j].text; j++) if(i >= story[j].s && i <= story[j].e) {
if(story[j].text[0] != '@')
caption = story[j].text;
else if(story[j].text[1] == 't')
dt = true;
else if(story[j].text[1] == 'n')
dn = true;
else if(story[j].text[2] == 'i')
fade = 255 * (i - story[j].s) / (story[j].e-story[j].s);
else if(story[j].text[2] == 'o')
fade = 255 * (story[j].e - i) / (story[j].e-story[j].s);
}
if(dt && drawtris < 255) drawtris++;
else if(drawtris && !dt) drawtris--;
linepatterns::patZebraTriangles.color = 0x40FF4000 + drawtris;
if(dn && drawnet < 255) drawnet++;
else if(drawnet && !dn) drawnet--;
linepatterns::patZebraLines.color = 0xFF000000 + drawnet;
vid.grid = drawnet;
history::phase = 1 + (isize(history::v)-3) * i * .95 / FRAMECOUNT;
history::movetophase();
char buf[500];
snprintf(buf, 500, fname.c_str(), i);
if(i == 0) drawthemap();
shmup::turn(100);
printf("%s\n", buf);
shot::shoty = 1080; shot::shotx = 1920;
shot::caption = caption;
shot::fade = fade;
shot::take(buf);
}
return;
}
}
#endif
string its05(int i) { char buf[64]; sprintf(buf, "%05d", i); return buf; }
int dimid(char x) {
if(x >= 'a' && x < 'a' + GDIM) return x - 'a';
else if(x >= '0' && x < '0' + GDIM) return x - '0';
else if(x >= 'x' && x < 'x' + GDIM) return x - 'x';
else {
println(hlog, "incorrect dimension ID");
throw hr_exception();
}
}
int readArgs() {
#if CAP_COMMANDLINE
using namespace arg;
if(0) ;
else if(argis("-collatz")) {
PHASE(3);
using namespace collatz;
shift(); sscanf(argcs(), "%lf,%lf,%lf,%lf", &s2, &p2, &s3, &p3);
start();
}
else if(argis("-collatz3")) {
PHASE(3);
using namespace collatz;
s2 = p2 = s3 = p3 = 0;
start();
transmatrix *T = &T2;
while(true) {
lshift();
if(arg::nomore()) break;
else if(argis("fd")) { shift(); *T = *T * xpush(argf()); }
else if(argcs()[0] == 't') { int x = dimid(argcs()[1]); int y = dimid(argcs()[2]); shift(); *T = *T * hr::cspin(x, y, argf()); }
else if(argis("/")) { if(T == &T2) T = &T3; else break; }
else break;
}
unshift();
}
else if(argis("-cshift")) {
shift_arg_formula(collatz::cshift);
}
else return 1;
#endif
return 0;
}
int ah = addHook(hooks_args, 100, readArgs) +
addHook_rvslides(42, [] (string s, vector<tour::slide>& v) {
if(s != "data") return;
using namespace tour;
v.push_back(
tour::slide{"Collatz conjecture", 51, LEGAL::UNLIMITED | QUICKGEO,
"The following slide is a visualization of the Collatz conjecture. "
"Press '5' for a spiral rendering of the Collatz conjecture visualization.\n\n"
"Note that this, and many other RogueViz visualizations, have "
"Euclidean versions (press ESC).\n",
pres::roguevizslide('d', [] () {
rogueviz::dftcolor = 0x206020FF;
int fac = euclid ? 2 : 1;
rogueviz::collatz::s2 = .3;
rogueviz::collatz::p2 = .5 * fac;
rogueviz::collatz::s3 = -.4;
rogueviz::collatz::p3 = .4 * fac;
rogueviz::showlabels = true;
gmatrix.clear();
drawthemap();
gmatrix0 = gmatrix;
rogueviz::collatz::start();
}, [] (presmode m) { slide_url(m, 'y', "YouTube link", "https://www.youtube.com/watch?v=NqPUwA_A0_k"); })
});
});
EX }
}
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