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hyperrogue/rogueviz/sunflower.cpp

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// non-Euclidean sunflower spirals (aka golden spirals or Fibonacci spirals)
// Copyright (C) 2018 Zeno and Tehora Rogue, see 'hyper.cpp' for details
// use: commandline parameter -sunflower <quantity> <density>
// e.g.: hyper -sunflower-qd 10000 1
// e.g.: hyper -sunflower-dr 1 4.5
// Commandlines for https://twitter.com/ZenoRogue/status/1247900522905886723 :
// Part 1:
// -geo 1 -sunflower-node 1 -sunflower-qd "1..10..20..60..100..140..180..220..|1000..1040..|2000..2040..|5000..5040..|10000..10040" 1 -zoom "sqrt(1000/(100+sunq))" -animperiod 20000 -shott 0 -back A0E0A0 -lw 16 -shotxy 1000 1000 -shotaa 2
// Part 2:
// -rugtsize 8192 -rugon -run -rugv 4000000 -run -sunflower-dr "0.001..0.002..0.005..0.01..0.02..0.04..0.06..0.07..0.08..0.09" 3..4.1..4.5..4.5..4.5..4.5..4.5..4.5..4.5 -lw 4 -sunflower-out 1 -shott 0 -back A0E0A0 -shotxy 1000 1000 -shotaa 2 -sunflower-adj 16 -animrec 600 curv%04d.png
// rotate the rug; press F10; wait until rug has millions of vertices; press F10; animation will be recorded
// Part 3:
// -rugtsize 8192 -rugon -rugv 1000000 -sunflower-dr .5 4.5 -lw 16 -shott 0 -back A0E0A0 -shotxy 1000 1000 -shotaa 2 -sunflower-adj 6
// (rotation animation set manually)
// Part 4:
// -geo 2 -sunflower-dr .1 pi -shott 0 -back A0E0A0 -shotxy 1000 1000 -shotaa 2 -animmove "2*pi" 0 0
#include "rogueviz.h"
namespace rogueviz {
namespace sunflower {
bool nodes;
ld qty = 100;
ld density = 1, zdensity;
ld range;
ld yshift;
ld distance_per_rug;
bool adjust_rug;
/* which property to infer from the other two: 'd'ensity, 'q'ty or 'r'ange */
char infer;
vector<hyperpoint> ps;
int iqty;
ld qfrac;
bool outward = false;
ld step_angle = M_PI * (3 - sqrt(5));
hyperpoint p(int i) {
ld step = step_angle;
return spin((outward ? i : i-iqty) * step) * xpush(sphere ? (acos(1 - (i+.5+qfrac) * density)) : euclid ? sqrt((i+.5+qfrac) * density) : acosh(1 + (i+.5+qfrac) * density)) * C0;
}
vector<int> inext, inext2;
vector<int> fibs;
color_t sunflower1 = 0xC04000FF;
color_t sunflower2 = 0xFFD500FF;
color_t sunflower3 = 0x000000FF;
bool overlay = false;
bool sunflower_cell(cell *c, shiftmatrix V) {
density = zdensity / 100;
ld qd;
if(sphere) {
if(infer == 'r')
range = qty * density * M_PI/2;
else qd = range * 2/M_PI;
}
else if(euclid) {
if(infer == 'r')
range = sqrt(qty * density);
else qd = range * range;
}
else {
if(infer == 'r')
range = acosh(1 + qty * density);
else
qd = (cosh(range) - 1);
}
if(infer == 'q') qty = qd / density;
if(infer == 'd') density = qd / qty;
if(adjust_rug) {
using namespace rug;
model_distance = sqrt(zdensity) * distance_per_rug;
}
iqty = qty;
qfrac = qty - iqty;
if(outward) qfrac = 0;
if(iqty < 0 || iqty > 2000000) return false;
if(fibs.empty()) {
ld best_error = 1;
vector<int> sgns;
for(int i=1; i<iqty; i++) {
ld v = i * step_angle / (2*M_PI);
v = frac(v);
auto sgn = v > .5;
if(sgn) v = 1-v;
if(v < best_error) fibs.push_back(i), sgns.push_back(sgn), best_error = v;
}
println(hlog, "fibs = ", fibs);
println(hlog, "sgns = ", sgns);
}
ps.resize(iqty);
inext.resize(iqty);
inext2.resize(iqty);
while(fibs.back() < iqty) {
/* to do: might not work correctly if step_angle is changed */
auto add = fibs.back() + *(fibs.end()-2);
fibs.push_back(add);
}
if(c == cwt.at) {
for(int i=0; i<iqty; i++) ps[i] = p(i);
for(int i=0; i<iqty; i++) {
ld ba = 99;
ld bb = 99;
int bi = 0, bj = 0;
for(int a: fibs) {
if(a>i) break;
if(hdist(ps[i], ps[i-a]) < ba)
bb = ba, bj = bi, ba = hdist(ps[i], ps[i-a]), bi = i-a;
else if(hdist(ps[i], ps[i-a]) < bb)
bb = hdist(ps[i], ps[i-a]), bj = i-a;
}
inext[i] = bi;
inext2[i] = bj;
}
if(sunflower1 || sunflower2 || sunflower3) for(int i=0; i<iqty; i++) {
if(inext[inext[i]] == inext2[i] || inext2[inext[i]] == inext2[i] || inext[inext2[i]] == inext[i] || inext2[inext2[i]] == inext[i]) {
curvepoint(ps[i]);
curvepoint(ps[inext2[i]]);
curvepoint(ps[inext[i]]);
// queuecurve(0xFFFFFFFF, 0x00C000FF, PPR::LINE);
queuecurve(V * ypush(yshift), sunflower3, sunflower1, PPR::LINE);
}
else {
curvepoint(ps[i]);
curvepoint(ps[inext[i]]);
curvepoint(ps[inext[i] + inext2[i] - i]);
curvepoint(ps[inext2[i]]);
queuecurve(V * ypush(yshift), sunflower3, sunflower2, PPR::LINE);
}
if(nodes) queuepolyat(V * ypush(yshift) * rgpushxto0(ps[i]), cgi.shSnowball, 0xFF, PPR::SUPERLINE);
}
}
return !overlay;
}
void insert_param() {
param_f(zdensity, "sund");
param_f(qty, "sunq");
param_f(range, "sunr");
param_f(distance_per_rug, "sunf");
param_f(yshift, "sunyshift");
}
void show();
void enable() {
rv_hook(hooks_o_key, 80, [] (o_funcs& v) { v.push_back(named_dialog("sunflowers", show)); });
rv_hook(hooks_drawcell, 100, sunflower_cell);
}
int readArgs() {
using namespace arg;
if(0) ;
else if(argis("-sunflower-qd")) {
enable();
infer = 'r';
shift_arg_formula(qty);
shift_arg_formula(zdensity);
patterns::whichShape = '9';
insert_param();
nohud = true;
}
else if(argis("-sunflower-qr")) {
enable();
infer = 'd';
shift_arg_formula(qty);
shift_arg_formula(range);
patterns::whichShape = '9';
insert_param();
nohud = true;
}
else if(argis("-sunflower-dr")) {
infer = 'q';
shift_arg_formula(zdensity);
shift_arg_formula(range);
enable();
/*
patterns::whichShape = '9';
*/
insert_param();
nohud = true;
}
else if(argis("-sunflower-node")) {
shift(); nodes = argi();
}
else if(argis("-sunflower-out")) {
shift(); outward = argi();
}
else if(argis("-sunflower-angle")) {
shift_arg_formula(step_angle, [] { fibs.clear(); });
}
else if(argis("-sunflower-adj")) {
adjust_rug = true;
shift_arg_formula(distance_per_rug);
}
else if(argis("-sunflower-colors")) {
PHASEFROM(2);
shift(); sunflower1 = argcolor(32);
shift(); sunflower2 = argcolor(32);
shift(); sunflower3 = argcolor(32);
}
else if(argis("-sunflower-overlay")) {
PHASEFROM(2);
shift(); overlay = argi();
}
else return 1;
return 0;
}
void show() {
cmode = sm::SIDE | sm::MAYDARK;
gamescreen(0);
dialog::init(XLAT("sunflower spirals"), 0xFFFFFFFF, 150, 0);
dialog::addSelItem("density", fts(zdensity), 'd');
dialog::add_action([] {
if(infer == 'd') infer = 'q';
dialog::editNumber(zdensity, 0, 2, .1, 1, "density", "density");
});
dialog::addSelItem("quantity", fts(qty), 'q');
dialog::add_action([] {
if(infer == 'q') infer = 'r';
dialog::editNumber(qty, 1, 100000, .1, 1000, "quantity", "quantity");
dialog::scaleLog();
});
dialog::addSelItem("radius", fts(range), 'q');
dialog::add_action([] {
if(infer == 'r') infer = 'd';
dialog::editNumber(range, 0, 10, .1, 2*M_PI, "range", "range");
dialog::scaleLog();
});
dialog::addSelItem("infer", infer == 'd' ? "density" : infer == 'q' ? "quantity" : "range", 'i');
dialog::add_action([] {
if(infer == 'r') infer = 'd';
else if(infer == 'd') infer = 'q';
else infer = 'r';
});
if(rug::rugged) {
dialog::addBoolItem("adjust Rug curvature", adjust_rug, 'a');
dialog::add_action([] {
adjust_rug = !adjust_rug;
distance_per_rug = rug::model_distance / sqrt(zdensity);
});
if(adjust_rug) {
dialog::addSelItem("factor", fts(distance_per_rug), 'f');
dialog::add_action([] {
dialog::editNumber(distance_per_rug, 0, 10, .1, 4,
"factor", "factor");
});
}
else {
dialog::addItem("disable the Hypersian Rug", 'f');
dialog::add_action(rug::close);
}
}
else {
dialog::addItem("enable the Hypersian Rug", 'a');
dialog::add_action(rug::init);
}
dialog::addBoolItem("draw the seeds", nodes, 's');
dialog::addBoolItem("grow at the edge", outward, 'o');
dialog::addBack();
dialog::display();
}
auto hook = 0
#if CAP_COMMANDLINE
+ addHook(hooks_args, 100, readArgs)
#endif
+ addHook_rvslides(144, [] (string s, vector<tour::slide>& v) {
if(s != "mixed") return;
using namespace tour;
v.push_back(
tour::slide{"sunflower spirals", 18, LEGAL::ANY | QUICKGEO,
"A sunflower sends out its n-th seed at angle 180° (3-sqrt(5)). "
"As new seeds are created, older seeds are pushed out. Therefore. "
"the distance d(n) of the n-th seed from the center will be such that "
"the area of a circle of radius d(n) changes linearly with n.\n\n"
"In the Euclidean plane, this process creates an interesting "
"phenomenon: if we try to compute the number of spirals at a given "
"distance from the center, we usually obtain a Fibonacci number. "
"The further from the start we are, the larger Fibonacci number we "
"get.\n\n"
"Because of the exponential growth in the hyperbolic plane, we "
"get to larger Fibonacci numbers faster.\n\n"
"Press 123 to change the geometry, 5 to see this in the Hypersian Rug model. "
"Press o to change the density.",
[] (presmode mode) {
slide_url(mode, 'y', "YouTube link", "https://www.youtube.com/watch?v=bKzibaNqEog");
slide_url(mode, 't', "Twitter link", "https://twitter.com/ZenoRogue/status/1247900522905886723");
setCanvas(mode, '0');
if((mode == pmStop || mode == pmGeometry) && rug::rugged) rug::close();
if(mode == pmKey) {
if(rug::rugged) rug::close();
else rug::init();
}
if(mode == pmStart) {
stop_game();
enable();
tour::slide_backup(range, sphere ? 2 : euclid ? 10 : 4.3);
tour::slide_backup<ld>(zdensity, 1);
tour::slide_backup(infer, 'q');
insert_param();
start_game();
}
}}
);
});
}
}
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