#include "../hyper.h" #include "rogueviz.h" namespace rogueviz { namespace collatz { double s2, s3, p2, p3; double cshift = -1; transmatrix T2, T3; edgetype *collatz1, *collatz2; int collatz_id; void start() { init(&collatz_id, 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); } void lookup(long long reached, int bits) { while(reached < (1ll< 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; ebase; 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(vizid != &collatz_id) return; 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; ibase, 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(vizid == &collatz_id) { sightrange_bonus = 3; genrange_bonus = 3; dronemode = true; vid.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= 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("-collatz-go")) { if(vizid != &collatz_id) { printf("not in Collatz\n"); throw hr_exception(); } 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 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(); } #if CAP_SHOT else if(argis("-rvvideo") && vizid == &collatz_id) { shift(); collatz_video(arg::args()); } #endif else if(argis("-cshift")) { shift_arg_formula(collatz::cshift); } else return 1; #endif return 0; } int ah = addHook(hooks_args, 100, readArgs) + addHook(rvtour::hooks_build_rvtour, 142, [] (vector& v) { using namespace tour; v.push_back( tour::slide{"unsorted/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", rvtour::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(); }) }); }) + addHook(hooks_drawvertex, 100, act); EX } }