Initial commit

figs/GFc.fig/GFc_gen.py

@@ -0,0 +1,290 @@
+#!/usr/bin/env python3
+
+import sys
+
+# This script generates a configuration of 3-staircases in which there is a
+# grid of particles in one phase, and the rest of space is filled with
+# particles in another phase.
+
+# size of grid
+L1=100
+L2=100
+
+# grid of particles in phase 1
+N11=12
+N12=12
+
+# position of lower left particle in phase 1
+x01=30+N12
+x02=30
+
+# only print from here to there
+l11=16
+l12=16
+l21=80
+l22=88
+
+# R2 of the model
+R2=3
+
+def main():
+    # particles in phase 1
+    particles1=[]
+    # particles in phase 2
+    particles2=[]
+
+    fill_particles1(particles1)
+    fill_particles2(particles2,particles1)
+
+    # join particles
+    particles=particles1+particles2
+
+    # compute which particles have a Voronoi cells containing a given site
+    voronoi_index=particles_in_voronoi(particles)
+    # compute the Voronoi cells of each particle
+    voronois=voronoi_of_particles(voronoi_index,particles)
+
+    # check whether the particles are in the GFc
+    GFc=particles_in_GFc(voronois,particles1,particles2)
+
+    # boundary of GFc
+    support=GFc_support(GFc,voronois)
+    GFc_boundary=boundary(support)
+
+    # print
+    print_headers()
+    print_particles(particles1,particles2,GFc)
+    print_boundary(GFc_boundary)
+    print_footers()
+
+# generate grid of particles in phase 1
+def fill_particles1(particles1):
+    for k1 in range(N11):
+        for k2 in range(N12):
+            particles1.append((x01+2*k1-k2,x02+k1+3*k2,1))
+
+# fill the rest of space with particles in phase 2
+def fill_particles2(particles2, particles1):
+    for x1 in range(L1):
+        for x2 in range(L2):
+            # index of particle
+            k1=(x1+3*x2)/7
+            k2=(2*x1-x2)/7
+
+            # check the indices are integers:
+            if k1 != int(k1) or k2 != int(k2):
+                continue
+
+            # check overlap with particles in phase 1
+            if check_overlap_1((x1,x2),particles1):
+                continue
+
+            particles2.append((x1,x2,2))
+
+# check overlap with particles in phase 1
+def check_overlap_1(x,particles1):
+    for p in particles1:
+        if check_overlap(x,p):
+            return True
+    return False
+
+# check overlap between two 3-staircases
+def check_overlap(x,y):
+    if max(abs(y[0]-x[0]),abs(y[1]-x[1]))>2:
+        return False
+    if abs((y[1]-x[1])+(y[0]-x[0]))<=2:
+        return True
+    return False
+
+
+# given a site, compute the particles whose Voronoi cell the site is in
+def particles_in_voronoi(particles):
+    out=[]
+    for x1 in range(L1):
+        for x2 in range(L2):
+            # minimize distance
+            mindist=L1+L2+1
+            candidate_list=[]
+            for p in particles:
+                dd=dist_support((x1,x2),p)
+                if dd<mindist:
+                    # reset candidate list
+                    candidate_list=[p]
+                    mindist=dd
+                elif dd==mindist:
+                    # append candidate
+                    candidate_list.append(p)
+
+            # add list to output (keep x1,x2 as index)
+            out.append(((x1,x2),candidate_list))
+    return out
+
+# distance between a point and the support of a particle
+def dist_support(x,p):
+    # if x is in support then 0
+    if abs(p[0]-x[0])+abs(p[1]-x[1])<=2 and x[0]>=p[0] and x[1]>=p[1]:
+        return 0
+
+    # base
+    out=abs(x[0]-p[0])+abs(x[1]-p[1])
+    # correct this depending on which site in \sigma_p is actually closest
+    # lower left quadrant: p is the closest
+    if x[0]-p[0]<=0 and x[1]-p[1]<=0:
+        return out
+    # lines next to lower left quadrant: neighbor of p closest
+    if x[0]-p[0]==1 and x[1]-p[1]<=0 or x[1]-p[1]==1 and x[0]-p[0]<=0:
+        return out-1
+    # otherwise: second neightbor of p closest
+    return out-2
+
+# from a table associating sites to voronoi cells, get particles
+def voronoi_of_particles(voronoi_index,particles):
+    out=[]
+    # output is indexed in the same order as particles
+    for p in particles:
+        vois=[]
+        for v in voronoi_index:
+            if p in v[1]:
+                vois.append(v[0])
+        out.append((p,vois))
+
+    return out
+
+# find which particles are in the GFc
+def particles_in_GFc(voronois,particles1,particles2):
+    out=[]
+    # loop over particles
+    for v in voronois:
+        # check all other particles
+        for w in voronois:
+            # skip v
+            if v==w:
+                continue
+            # check whether the distance between the cells is <=R2
+            if set_dist(v[1],w[1])>R2:
+                continue
+            # check whether w is #-correct
+            if not ((w[0][2]==1 and sharp_correct1(w[0],particles1)) or (w[0][2]==2 and sharp_correct2(w[0],particles2))):
+                # in GFc
+                out.append(v[0])
+                break
+
+    return out
+                
+
+# distance between two sets
+def set_dist(s1,s2):
+    if len(s1)==0 or len(s2)==0:
+        print("error: computing the distance between two sets, one of which is empty",file=sys.stderr)
+        exit(-1)
+        return -1
+    mind=abs(s1[0][0]-s2[0][0])+abs(s1[0][1]-s2[0][1])
+    for x in s1:
+        for y in s2:
+            if abs(x[0]-y[0])+abs(x[1]-y[1])<mind:
+                mind=abs(x[0]-y[0])+abs(x[1]-y[1])
+    return mind
+
+# check whether a particle of type 1 is #-correct:
+def sharp_correct1(x,particles1):
+    if (x[0]+2,x[1]+1,1) not in particles1:
+        return False
+    if (x[0]-2,x[1]-1,1) not in particles1:
+        return False
+    if (x[0]-3,x[1]+2,1) not in particles1:
+        return False
+    if (x[0]+3,x[1]-2,1) not in particles1:
+        return False
+    if (x[0]+1,x[1]-3,1) not in particles1:
+        return False
+    if (x[0]-1,x[1]+3,1) not in particles1:
+        return False
+    return True
+
+# check whether a particle of type 2 is #-correct:
+def sharp_correct2(x,particles2):
+    if (x[0]+1,x[1]+2,2) not in particles2:
+        return False
+    if (x[0]-1,x[1]-2,2) not in particles2:
+        return False
+    if (x[0]+2,x[1]-3,2) not in particles2:
+        return False
+    if (x[0]-2,x[1]+3,2) not in particles2:
+        return False
+    if (x[0]-3,x[1]+1,2) not in particles2:
+        return False
+    if (x[0]+3,x[1]-1,2) not in particles2:
+        return False
+    return True
+
+
+# support of a GFc
+def GFc_support(GFc,voronois):
+    out=[]
+    for p in GFc:
+        # find Voronoi cell
+        for v in voronois:
+            if p==v[0]:
+                out=out+v[1]
+                break
+
+    # remove duplicates
+    return list(set(out))
+
+# boundary of a set
+def boundary(S):
+    out=[]
+    for s in S:
+        if (s[0]+1,s[1]) not in S:
+            out.append(((s[0]+0.5,s[1]-0.5),(s[0]+0.5,s[1]+0.5)))
+        if (s[0]-1,s[1]) not in S:
+            out.append(((s[0]-0.5,s[1]-0.5),(s[0]-0.5,s[1]+0.5)))
+        if (s[0],s[1]+1) not in S:
+            out.append(((s[0]-0.5,s[1]+0.5),(s[0]+0.5,s[1]+0.5)))
+        if (s[0],s[1]-1) not in S:
+            out.append(((s[0]-0.5,s[1]-0.5),(s[0]+0.5,s[1]-0.5)))
+    return out
+
+
+# print particles
+def print_headers():
+    print(r'''\documentclass{standalone}
+
+\usepackage{tikz}
+\usepackage{shapes}
+
+\begin{document}
+\begin{tikzpicture}
+
+''')
+    
+    # print grid
+    print(r'\grid{'+str(l21-l11+1+3)+'}{'+str(l22-l12+1+3)+'}{('+str(l11-1)+','+str(l12-1)+')}')
+
+def print_particles(particles1,particles2,GFc):
+    for p in particles1:
+        if p[0]>=l11 and p[0]<=l21 and p[1]>=l12 and p[1]<=l22:
+            if p in GFc:
+                print(r'\staircase{green}{('+str(p[0])+','+str(p[1])+')}')
+            else:
+                print(r'\staircase{cyan}{('+str(p[0])+','+str(p[1])+')}')
+    for p in particles2:
+        if p[0]>=l11 and p[0]<=l21 and p[1]>=l12 and p[1]<=l22:
+            if p in GFc:
+                print(r'\staircase{yellow}{('+str(p[0])+','+str(p[1])+')}')
+            else:
+                print(r'\staircase{red}{('+str(p[0])+','+str(p[1])+')}')
+
+def print_boundary(boundary):
+    for seg in boundary:
+        if seg[0][0]>=l11 and seg[0][0]<=l21 and seg[0][1]>=l12 and seg[0][1]<=l22:
+            if seg[1][0]>=l11 and seg[1][0]<=l21 and seg[1][1]>=l12 and seg[1][1]<=l22:
+                print(r'\draw[line width=8pt]('+str(seg[0][0])+','+str(seg[0][1])+')--('+str(seg[1][0])+','+str(seg[1][1])+');')
+
+def print_footers():
+    print(r'''
+
+\end{tikzpicture}
+\end{document}''')
+
+main()

figs/GFc.fig/Makefile

@@ -0,0 +1,31 @@
+PROJECTNAME=GFc
+LIBS=$(notdir $(wildcard libs/*))
+
+PDFS=$(addsuffix .pdf, $(PROJECTNAME))
+
+all: $(PDFS)
+
+$(PDFS): $(LIBS) GFc.tikz.tex
+	pdflatex -jobname $(basename $@) -file-line-error $(patsubst %.pdf, %.tikz.tex, $@)
+
+GFc.tikz.tex:
+	python3 GFc_gen.py > GFc.tikz.tex
+
+install: $(PDFS)
+	cp $^ $(INSTALLDIR)/
+
+$(LIBS):
+	ln -fs libs/$@ ./
+
+clean-libs:
+	rm -f $(LIBS)
+
+clean-aux:
+	rm -f $(addsuffix .aux, $(PROJECTNAME))
+	rm -f $(addsuffix .log, $(PROJECTNAME))
+
+clean-tex:
+	rm -f $(PDFS)
+	rm -f GFc.tikz.tex
+
+clean: clean-libs clean-aux clean-tex

figs/GFc.fig/shapes.sty

@@ -0,0 +1 @@
+../libs/shapes.sty

figs/boundary_rconnected.fig/Makefile

@@ -0,0 +1 @@
+../libs/Makefile

figs/boundary_rconnected.fig/boundary_rconnected.tikz.tex

@@ -0,0 +1,43 @@
+\documentclass{standalone}
+
+\usepackage{tikz}
+\usepackage{shapes}
+
+\begin{document}
+\begin{tikzpicture}
+  \grid{10}{10}{(0,0)}
+
+  \fill[color=gray](1.5,1.5)--++(5,0)--++(0,3)--++(2,0)--++(0,2)--++(-5,0)--++(0,2)--++(-2,0);
+
+  \fill[color=red](2,1)circle(0.1);
+  \fill[color=red](3,1)circle(0.1);
+  \fill[color=red](4,1)circle(0.1);
+  \fill[color=red](5,1)circle(0.1);
+  \fill[color=red](6,1)circle(0.1);
+  \fill[color=red](7,2)circle(0.1);
+  \fill[color=red](7,3)circle(0.1);
+  \fill[color=red](7,4)circle(0.1);
+  \fill[color=red](8,4)circle(0.1);
+  \fill[color=red](9,5)circle(0.1);
+  \fill[color=red](9,6)circle(0.1);
+  \fill[color=red](8,7)circle(0.1);
+  \fill[color=red](7,7)circle(0.1);
+  \fill[color=red](6,7)circle(0.1);
+  \fill[color=red](5,7)circle(0.1);
+  \fill[color=red](4,7)circle(0.1);
+  \fill[color=red](4,8)circle(0.1);
+  \fill[color=red](3,9)circle(0.1);
+  \fill[color=red](2,9)circle(0.1);
+  \fill[color=red](1,8)circle(0.1);
+  \fill[color=red](1,7)circle(0.1);
+  \fill[color=red](1,6)circle(0.1);
+  \fill[color=red](1,5)circle(0.1);
+  \fill[color=red](1,4)circle(0.1);
+  \fill[color=red](1,3)circle(0.1);
+  \fill[color=red](1,2)circle(0.1);
+
+\draw[color=red, dotted, line width=2pt](2,1)--(3,1)--(4,1)--(5,1)--(6,1)--(7,2)--(7,3)--(7,4)--(8,4)--(9,5)--(9,6)--(8,7)--(7,7)--(6,7)--(5,7)--(4,7)--(4,8)--(3,9)--(2,9)--(1,8)--(1,7)--(1,6)--(1,5)--(1,4)--(1,3)--(1,2)--cycle;
+
+\end{tikzpicture}
+\end{document}
+

figs/boundary_rconnected.fig/shapes.sty

@@ -0,0 +1 @@
+../libs/shapes.sty

figs/disk.fig/Makefile

@@ -0,0 +1 @@
+../libs/Makefile

figs/disk.fig/disk.tikz.tex

@@ -0,0 +1,13 @@
+\documentclass{standalone}
+
+\usepackage{tikz}
+\usepackage{shapes}
+
+\begin{document}
+\begin{tikzpicture}
+  \grid{6}{6}{(-3,-3)}
+
+  \disk{cyan}{(0,0)}
+\end{tikzpicture}
+\end{document}
+

figs/disk.fig/disk_max_1.tikz.tex

@@ -0,0 +1,19 @@
+\documentclass{standalone}
+
+\usepackage{tikz}
+\usepackage{shapes}
+
+\begin{document}
+\begin{tikzpicture}
+  \grid{6}{11}{(-3,-3)}
+
+  \square{yellow}{(-2,2)}
+  \square{yellow}{(2,2)}
+
+  \disk{cyan}{(0,0)}
+
+  \disk{magenta}{(0,5)}
+
+\end{tikzpicture}
+\end{document}
+

figs/disk.fig/disk_max_2.tikz.tex

@@ -0,0 +1,19 @@
+\documentclass{standalone}
+
+\usepackage{tikz}
+\usepackage{shapes}
+
+\begin{document}
+\begin{tikzpicture}
+  \grid{7}{11}{(-3,-3)}
+
+  \square{green}{(-1,3)}
+  \square{green}{(2,2)}
+
+  \disk{cyan}{(0,0)}
+
+  \disk{magenta}{(1,5)}
+
+\end{tikzpicture}
+\end{document}
+

figs/disk.fig/disk_neighbors.tikz.tex

@@ -0,0 +1,32 @@
+\documentclass{standalone}
+
+\usepackage{tikz}
+\usepackage{shapes}
+
+\begin{document}
+\begin{tikzpicture}
+  \grid{8}{8}{(-4,-4)}
+
+  \square{green}{(-1,3)}
+  \square{green}{(0,3)}
+  \square{green}{(1,3)}
+  \square{green}{(3,-1)}
+  \square{green}{(3,0)}
+  \square{green}{(3,1)}
+  \square{green}{(-1,-3)}
+  \square{green}{(0,-3)}
+  \square{green}{(1,-3)}
+  \square{green}{(-3,-1)}
+  \square{green}{(-3,0)}
+  \square{green}{(-3,1)}
+
+  \square{green}{(2,2)}
+  \square{green}{(2,-2)}
+  \square{green}{(-2,2)}
+  \square{green}{(-2,-2)}
+
+  \disk{cyan}{(0,0)}
+
+\end{tikzpicture}
+\end{document}
+

figs/disk.fig/disk_pack_1.tikz.tex

@@ -0,0 +1,28 @@
+\documentclass{standalone}
+
+\usepackage{tikz}
+\usepackage{shapes}
+
+\begin{document}
+\begin{tikzpicture}
+  \grid{16}{16}{(-8,-8)}
+
+  \square{green}{(2,2)}
+  \square{green}{(0,3)}
+  \square{green}{(-3,1)}
+  \square{green}{(-2,-2)}
+  \square{green}{(0,-3)}
+  \square{green}{(3,-1)}
+
+  \disk{cyan}{(0,0)}
+
+  \disk{magenta}{(5,1)}
+  \disk{magenta}{(2,5)}
+  \disk{magenta}{(-3,4)}
+  \disk{magenta}{(-5,-1)}
+  \disk{magenta}{(-2,-5)}
+  \disk{magenta}{(3,-4)}
+
+\end{tikzpicture}
+\end{document}
+

figs/disk.fig/disk_pack_2.tikz.tex

@@ -0,0 +1,26 @@
+\documentclass{standalone}
+
+\usepackage{tikz}
+\usepackage{shapes}
+
+\begin{document}
+\begin{tikzpicture}
+  \grid{16}{16}{(-8,-8)}
+
+  \square{yellow}{(2,2)}
+  \square{yellow}{(-2,2)}
+  \square{green}{(0,-3)}
+  \square{green}{(3,-1)}
+  \square{green}{(-3,-1)}
+
+  \disk{cyan}{(0,0)}
+
+  \disk{magenta}{(0,5)}
+  \disk{magenta}{(5,1)}
+  \disk{magenta}{(-5,1)}
+  \disk{magenta}{(3,-4)}
+  \disk{magenta}{(-3,-4)}
+
+\end{tikzpicture}
+\end{document}
+

figs/disk.fig/octagon.tikz.tex

@@ -0,0 +1,13 @@
+\documentclass{standalone}
+
+\usepackage{tikz}
+\usepackage{shapes}
+
+\begin{document}
+\begin{tikzpicture}
+  \grid{6}{6}{(-3,-3)}
+
+  \octagon{cyan}{(0,0)}
+\end{tikzpicture}
+\end{document}
+

figs/disk.fig/shapes.sty

@@ -0,0 +1 @@
+../libs/shapes.sty

figs/libs/Makefile

@@ -0,0 +1,28 @@
+PROJECTNAME=$(basename $(basename $(wildcard *.tikz.tex)))
+LIBS=$(notdir $(wildcard libs/*))
+
+PDFS=$(addsuffix .pdf, $(PROJECTNAME))
+
+all: $(PDFS)
+
+$(PDFS): $(LIBS)
+	echo $(LIBS)
+	pdflatex -jobname $(basename $@) -file-line-error $(patsubst %.pdf, %.tikz.tex, $@)
+
+install: $(PDFS)
+	cp $^ $(INSTALLDIR)/
+
+$(LIBS):
+	ln -fs libs/$@ ./
+
+clean-libs:
+	rm -f $(LIBS)
+
+clean-aux:
+	rm -f $(addsuffix .aux, $(PROJECTNAME))
+	rm -f $(addsuffix .log, $(PROJECTNAME))
+
+clean-tex:
+	rm -f $(PDFS)
+
+clean: clean-libs clean-aux clean-tex

figs/libs/shapes.sty

@@ -0,0 +1,81 @@
+% square lattice (width #1, height #2, origin #3, spacing #4)
+\def\grid#1#2#3{
+  \foreach\i in {0,...,#2}{
+    \draw#3++(0,\i)--++(#1,0);
+  }
+  \foreach\i in {0,...,#1}{
+    \draw#3++(\i,0)--++(0,#2);
+  }
+}
+
+
+% 3-staircase (color #1, position #2)
+% speedup
+\def\staircase#1#2{
+  \fill[color=#1]#2++(-0.5,-0.5)--++(3,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,-3);
+  \draw[color=white]#2++(-0.5,0)--++(3,0);
+  \draw[color=white]#2++(-0.5,1)--++(2,0);
+  \draw[color=white]#2++(-0.5,2)--++(1,0);
+  \draw[color=white]#2++(0,-0.5)--++(0,3);
+  \draw[color=white]#2++(1,-0.5)--++(0,2);
+  \draw[color=white]#2++(2,-0.5)--++(0,1);
+  \draw[color=black]#2++(-0.5,-0.5)--++(3,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,-3);
+}
+%\def\staircase#1#2{
+%  \fill[color=#1]#2++(-0.5,-0.5)--++(3,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,-3);
+%  \begin{scope}
+%    \clip#2++(-0.5,-0.5)--++(3,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,-3);
+%    \grid44{[color=white]#2++(-1,-1)}
+%  \end{scope}
+%  \draw[color=black]#2++(-0.5,-0.5)--++(3,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,-3);
+%}
+
+% 4-staircase (color #1, position #2)
+\def\Staircase#1#2{
+  \fill[color=#1]#2++(-0.5,-0.5)--++(4,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,-4);
+  \begin{scope}
+    \clip#2++(-0.5,-0.5)--++(4,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,-4);
+    \grid55{[color=white]#2++(-1,-1)}
+  \end{scope}
+  \draw[color=black]#2++(-0.5,-0.5)--++(4,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,-4);
+}
+
+% 5-staircase (color #1, position #2)
+\def\staircaseV#1#2{
+  \fill[color=#1]#2++(-0.5,-0.5)--++(5,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,-5);
+  \begin{scope}
+    \clip#2++(-0.5,-0.5)--++(5,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,-5);
+    \grid55{[color=white]#2++(-1,-1)}
+  \end{scope}
+  \draw[color=black]#2++(-0.5,-0.5)--++(5,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,-5);
+}
+
+% square (color #1, position #2)
+\def\square#1#2{
+  \fill[color=#1]#2++(-0.5,-0.5)--++(1,0)--++(0,1)--++(-1,0)--++(0,-1);
+  \begin{scope}
+    \clip#2++(-0.5,-0.5)--++(1,0)--++(0,1)--++(-1,0)--++(0,-1);
+    \grid22{[color=white]#2++(-1,-1)}
+  \end{scope}
+  %\draw[color=black]#2++(-0.5,-0.5)--++(1,0)--++(0,1)--++(-1,0)--++(0,-1);
+}
+
+% disk (color #1, position #2)
+\def\disk#1#2{
+  \fill[color=#1]#2circle(2.5);
+  \begin{scope}
+    \clip#2circle(2.5);
+    \grid66{[color=white]#2++(-3,-3)}
+  \end{scope}
+  \draw[color=black]#2circle(2.5);
+}
+
+% octagon (color #1, position #2)
+\def\octagon#1#2{
+  \fill[color=#1]#2++(-1,-2.5)--++(2,0)--++(1.5,1.5)--++(0,2)--++(-1.5,1.5)--++(-2,0)--++(-1.5,-1.5)--++(0,-2)--++(1.5,-1.5);
+  \begin{scope}
+    \clip#2++(-1,-2.5)--++(2,0)--++(1.5,1.5)--++(0,2)--++(-1.5,1.5)--++(-2,0)--++(-1.5,-1.5)--++(0,-2)--++(1.5,-1.5);
+    \grid66{[color=white]#2++(-3,-3)}
+  \end{scope}
+  \draw[color=black]#2++(-1,-2.5)--++(2,0)--++(1.5,1.5)--++(0,2)--++(-1.5,1.5)--++(-2,0)--++(-1.5,-1.5)--++(0,-2)--++(1.5,-1.5);
+}

figs/nstaircase.fig/5staircase_case_1-1.tikz.tex

@@ -0,0 +1,20 @@
+\documentclass{standalone}
+
+\usepackage{tikz}
+\usepackage{shapes}
+
+\begin{document}
+\begin{tikzpicture}
+  \grid{10}{10}{(-1,-1)}
+
+  \staircaseV{blue}{(0,0)}
+  \staircaseV{green}{(2,3)}
+
+  \square{gray}{(1,4)}
+  \square{gray}{(3,2)}
+  \square{gray}{(4,1)}
+  \square{gray}{(4,2)}
+
+\end{tikzpicture}
+\end{document}
+

figs/nstaircase.fig/5staircase_case_1-2.tikz.tex

@@ -0,0 +1,25 @@
+\documentclass{standalone}
+
+\usepackage{tikz}
+\usepackage{shapes}
+
+\begin{document}
+\begin{tikzpicture}
+  \grid{10}{10}{(-1,-1)}
+
+  \staircaseV{blue}{(0,0)}
+  \staircaseV{green}{(3,4)}
+  
+  \square{lightgray}{(3,3)}
+  \square{lightgray}{(4,3)}
+
+  \square{gray}{(1,4)}
+  \square{gray}{(2,3)}
+  \square{gray}{(2,4)}
+  \square{gray}{(3,2)}
+  \square{gray}{(4,1)}
+  \square{gray}{(4,2)}
+
+\end{tikzpicture}
+\end{document}
+

figs/nstaircase.fig/5staircase_case_1-3.tikz.tex

@@ -0,0 +1,26 @@
+\documentclass{standalone}
+
+\usepackage{tikz}
+\usepackage{shapes}
+
+\begin{document}
+\begin{tikzpicture}
+  \grid{10}{10}{(-1,-1)}
+
+  \staircaseV{blue}{(0,0)}
+
+  \square{lightgray}{(2,4)}
+  \square{lightgray}{(3,4)}
+  \square{lightgray}{(4,2)}
+  \square{lightgray}{(4,3)}
+  \square{lightgray}{(4,4)}
+
+  \square{gray}{(1,4)}
+  \square{gray}{(2,3)}
+  \square{gray}{(3,2)}
+  \square{gray}{(3,3)}
+  \square{gray}{(4,1)}
+
+\end{tikzpicture}
+\end{document}
+

figs/nstaircase.fig/5staircase_case_2-1.tikz.tex

@@ -0,0 +1,20 @@
+\documentclass{standalone}
+
+\usepackage{tikz}
+\usepackage{shapes}
+
+\begin{document}
+\begin{tikzpicture}
+  \grid{14}{10}{(-9,-1)}
+
+  \staircaseV{blue}{(0,0)}
+  \staircaseV{green}{(-5,2)}
+
+  \square{gray}{(-2,4)}
+  \square{gray}{(-1,1)}
+  \square{gray}{(-1,3)}
+  \square{gray}{(-1,4)}
+
+\end{tikzpicture}
+\end{document}
+

figs/nstaircase.fig/5staircase_case_2-2.tikz.tex

@@ -0,0 +1,26 @@
+\documentclass{standalone}
+
+\usepackage{tikz}
+\usepackage{shapes}
+
+\begin{document}
+\begin{tikzpicture}
+  \grid{14}{10}{(-9,-1)}
+
+  \staircaseV{blue}{(0,0)}
+  \staircaseV{green}{(-8,4)}
+
+  \square{lightgray}{(-3,3)}
+  \square{lightgray}{(-2,2)}
+
+  \square{gray}{(-3,4)}
+  \square{gray}{(-2,3)}
+  \square{gray}{(-2,4)}
+  \square{gray}{(-1,1)}
+  \square{gray}{(-1,2)}
+  \square{gray}{(-1,3)}
+  \square{gray}{(-1,4)}
+
+\end{tikzpicture}
+\end{document}
+

figs/nstaircase.fig/5staircase_case_2-3.tikz.tex

@@ -0,0 +1,26 @@
+\documentclass{standalone}
+
+\usepackage{tikz}
+\usepackage{shapes}
+
+\begin{document}
+\begin{tikzpicture}
+  \grid{14}{10}{(-9,-1)}
+
+  \staircaseV{blue}{(0,0)}
+
+  \square{lightgray}{(-4,4)}
+  \square{lightgray}{(-3,3)}
+  \square{lightgray}{(-3,4)}
+  \square{lightgray}{(-2,2)}
+  \square{lightgray}{(-2,4)}
+
+  \square{gray}{(-2,3)}
+  \square{gray}{(-1,1)}
+  \square{gray}{(-1,2)}
+  \square{gray}{(-1,3)}
+  \square{gray}{(-1,4)}
+
+\end{tikzpicture}
+\end{document}
+

figs/nstaircase.fig/5staircase_regions.tikz.tex

@@ -0,0 +1,48 @@
+\documentclass{standalone}
+
+\usepackage{tikz}
+\usepackage{shapes}
+
+\begin{document}
+\begin{tikzpicture}
+  \grid{10}{10}{(-5,-5)}
+
+  \staircaseV{blue}{(0,0)}
+
+  \square{lightgray}{(-4,4)}
+  \square{lightgray}{(-3,3)}
+  \square{lightgray}{(-3,4)}
+  \square{lightgray}{(-2,2)}
+  \square{lightgray}{(-2,3)}
+  \square{lightgray}{(-2,4)}
+  \square{lightgray}{(-1,1)}
+  \square{lightgray}{(-1,2)}
+  \square{lightgray}{(-1,3)}
+  \square{lightgray}{(-1,4)}
+  
+  \square{lightgray}{(1,4)}
+  \square{lightgray}{(2,3)}
+  \square{lightgray}{(2,4)}
+  \square{lightgray}{(3,2)}
+  \square{lightgray}{(3,3)}
+  \square{lightgray}{(3,4)}
+  \square{lightgray}{(4,1)}
+  \square{lightgray}{(4,2)}
+  \square{lightgray}{(4,3)}
+  \square{lightgray}{(4,4)}
+  
+  \square{lightgray}{(1,-1)}
+  \square{lightgray}{(2,-2)}
+  \square{lightgray}{(2,-1)}
+  \square{lightgray}{(3,-3)}
+  \square{lightgray}{(3,-2)}
+  \square{lightgray}{(3,-1)}
+  \square{lightgray}{(4,-4)}
+  \square{lightgray}{(4,-3)}
+  \square{lightgray}{(4,-2)}
+  \square{lightgray}{(4,-1)}
+
+
+\end{tikzpicture}
+\end{document}
+

figs/nstaircase.fig/Makefile

@@ -0,0 +1 @@
+../libs/Makefile

figs/nstaircase.fig/shapes.sty

@@ -0,0 +1 @@
+../libs/shapes.sty

figs/nstaircase.fig/upper_triangular_boundary.tikz.tex

@@ -0,0 +1,39 @@
+\documentclass{standalone}
+
+\usepackage{tikz}
+\usepackage{shapes}
+
+\begin{document}
+\begin{tikzpicture}
+  \grid{7}{7}{(-1,-1)}
+
+  \square{gray}{(1,4)}
+  \square{gray}{(2,3)}
+  \square{gray}{(2,4)}
+  \square{gray}{(3,2)}
+  \square{gray}{(3,3)}
+  \square{gray}{(3,4)}
+  \square{gray}{(4,1)}
+  \square{gray}{(4,2)}
+  \square{gray}{(4,3)}
+  \square{gray}{(4,4)}
+  
+  \square{yellow}{(0,4)}
+  \square{yellow}{(1,3)}
+  \square{yellow}{(2,2)}
+  \square{yellow}{(3,1)}
+  \square{yellow}{(4,0)}
+  
+  \square{magenta}{(5,1)}
+  \square{magenta}{(5,2)}
+  \square{magenta}{(5,3)}
+  \square{magenta}{(5,4)}
+
+  \square{green}{(1,5)}
+  \square{green}{(2,5)}
+  \square{green}{(3,5)}
+  \square{green}{(4,5)}
+
+\end{tikzpicture}
+\end{document}
+

figs/staircases.fig/3staircase.tikz.tex

@@ -0,0 +1,13 @@
+\documentclass{standalone}
+
+\usepackage{tikz}
+\usepackage{shapes}
+
+\begin{document}
+\begin{tikzpicture}
+  \grid{4}{4}{(-1,-1)}
+
+  \staircase{cyan}{(0,0)}
+\end{tikzpicture}
+\end{document}
+

figs/staircases.fig/3staircase_ground_state.tikz.tex

@@ -0,0 +1,20 @@
+\documentclass{standalone}
+
+\usepackage{tikz}
+\usepackage{shapes}
+
+\begin{document}
+\begin{tikzpicture}
+
+  \clip(-2,6)--++(12,0)--++(0,12)--++(-12,0);
+
+  \grid{19}{24}{(-6,-1)}
+  \foreach\x in {0,...,6}{
+    \foreach\y in {0,...,6}{
+      \staircase{cyan}{(2*\x-\y,\x+3*\y)}
+    }
+  }
+
+\end{tikzpicture}
+\end{document}
+

figs/staircases.fig/3staircase_max.tikz.tex

@@ -0,0 +1,27 @@
+\documentclass{standalone}
+
+\usepackage{tikz}
+\usepackage{shapes}
+
+\begin{document}
+\begin{tikzpicture}
+  \grid{6}{6}{(-2,-2)}
+
+  \staircase{cyan}{(0,0)}
+
+  \square{green}{(0,-1)}
+  \square{green}{(1,-1)}
+  \square{green}{(2,-1)}
+
+  \square{magenta}{(-1,0)}
+  \square{magenta}{(-1,1)}
+  \square{magenta}{(-1,2)}
+
+  \square{yellow}{(1,2)}
+  \square{yellow}{(2,1)}
+
+  \square{lightgray}{(0,3)}
+  \square{lightgray}{(3,0)}
+\end{tikzpicture}
+\end{document}
+

figs/staircases.fig/3staircase_pack.tikz.tex

@@ -0,0 +1,25 @@
+\documentclass{standalone}
+
+\usepackage{tikz}
+\usepackage{shapes}
+
+\begin{document}
+\begin{tikzpicture}
+  \grid{10}{10}{(-4,-4)}
+
+  \staircase{cyan}{(0,0)}
+
+  \staircase{magenta}{(2,1)}
+  \staircase{magenta}{(-2,-1)}
+  \staircase{magenta}{(-3,2)}
+  \staircase{magenta}{(3,-2)}
+  \staircase{magenta}{(1,-3)}
+  \staircase{magenta}{(-1,3)}
+
+  \square{green}{(2,-1)}
+  \square{green}{(-1,1)}
+  \square{green}{(1,2)}
+
+\end{tikzpicture}
+\end{document}
+

figs/staircases.fig/4staircase.tikz.tex

@@ -0,0 +1,13 @@
+\documentclass{standalone}
+
+\usepackage{tikz}
+\usepackage{shapes}
+
+\begin{document}
+\begin{tikzpicture}
+  \grid{5}{5}{(-1,-1)}
+
+  \Staircase{cyan}{(0,0)}
+\end{tikzpicture}
+\end{document}
+

figs/staircases.fig/4staircase_max.tikz.tex

@@ -0,0 +1,31 @@
+\documentclass{standalone}
+
+\usepackage{tikz}
+\usepackage{shapes}
+
+\begin{document}
+\begin{tikzpicture}
+  \grid{7}{7}{(-2,-2)}
+
+  \Staircase{cyan}{(0,0)}
+
+  \square{green}{(0,-1)}
+  \square{green}{(1,-1)}
+  \square{green}{(2,-1)}
+  \square{green}{(3,-1)}
+
+  \square{magenta}{(-1,0)}
+  \square{magenta}{(-1,1)}
+  \square{magenta}{(-1,2)}
+  \square{magenta}{(-1,3)}
+
+  \square{yellow}{(3,1)}
+  \square{yellow}{(2,2)}
+  \square{yellow}{(1,3)}
+
+  \square{lightgray}{(0,4)}
+  \square{lightgray}{(4,0)}
+
+\end{tikzpicture}
+\end{document}
+

figs/staircases.fig/4staircase_pack.tikz.tex

@@ -0,0 +1,28 @@
+\documentclass{standalone}
+
+\usepackage{tikz}
+\usepackage{shapes}
+
+\begin{document}
+\begin{tikzpicture}
+  \grid{13}{13}{(-5,-5)}
+
+  \Staircase{cyan}{(0,0)}
+
+  \Staircase{magenta}{(2,2)}
+  \Staircase{magenta}{(-2,4)}
+  \Staircase{magenta}{(-4,2)}
+  \Staircase{magenta}{(-2,-2)}
+  \Staircase{magenta}{(2,-4)}
+  \Staircase{magenta}{(4,-2)}
+
+  \square{green}{(1,-1)}
+  \square{green}{(3,-1)}
+  \square{green}{(3,1)}
+  \square{green}{(-1,1)}
+  \square{green}{(-1,3)}
+  \square{green}{(1,3)}
+
+\end{tikzpicture}
+\end{document}
+

figs/staircases.fig/Makefile

@@ -0,0 +1 @@
+../libs/Makefile

figs/staircases.fig/shapes.sty

@@ -0,0 +1 @@
+../libs/shapes.sty