From bdf817efec1cfdd67cc6176a6664442fd98173ae Mon Sep 17 00:00:00 2001
From: Ian Jauslin <ian@jauslin.org>
Date: Mon, 17 Oct 2022 20:59:01 -0400
Subject: As presented at RUMA on 2022-10-12

---
 figs/atoms.fig/Makefile              |  15 +++++
 figs/atoms.fig/crystal-base.gp       |  21 +++++++
 figs/atoms.fig/crystal.py            |  24 ++++++++
 figs/atoms.fig/gas-base.gp           |  21 +++++++
 figs/atoms.fig/gas-rods-base.gp      |  21 +++++++
 figs/atoms.fig/gas-rods.py           |  88 ++++++++++++++++++++++++++++
 figs/atoms.fig/gas.py                |  39 +++++++++++++
 figs/atoms.fig/liquid-base.gp        |  21 +++++++
 figs/atoms.fig/liquid.py             |  39 +++++++++++++
 figs/atoms.fig/nematic-base.gp       |  21 +++++++
 figs/atoms.fig/nematic.py            |  90 +++++++++++++++++++++++++++++
 figs/atoms.fig/smectic-base.gp       |  21 +++++++
 figs/atoms.fig/smectic.py            |  92 +++++++++++++++++++++++++++++
 figs/diamonds.fig/Makefile           |  20 +++++++
 figs/diamonds.fig/diamonds.py        |  65 +++++++++++++++++++++
 figs/diamonds.fig/shapes.sty         |   1 +
 figs/libs/shapes.sty                 | 109 +++++++++++++++++++++++++++++++++++
 figs/rods.fig/Makefile               |  28 +++++++++
 figs/rods.fig/libs/shapes.sty        |   1 +
 figs/rods.fig/rods.tikz.tex          |  30 ++++++++++
 figs/shapes.fig/L_tetromino.tikz.tex |  11 ++++
 figs/shapes.fig/Makefile             |  28 +++++++++
 figs/shapes.fig/P_pentomino.tikz.tex |  11 ++++
 figs/shapes.fig/T_tetromino.tikz.tex |  11 ++++
 figs/shapes.fig/V_triomino.tikz.tex  |  11 ++++
 figs/shapes.fig/cross.tikz.tex       |  11 ++++
 figs/shapes.fig/diamond.tikz.tex     |  11 ++++
 figs/shapes.fig/hexagon.tikz.tex     |  37 ++++++++++++
 figs/shapes.fig/libs/shapes.sty      |   1 +
 29 files changed, 899 insertions(+)
 create mode 100644 figs/atoms.fig/Makefile
 create mode 100644 figs/atoms.fig/crystal-base.gp
 create mode 100644 figs/atoms.fig/crystal.py
 create mode 100644 figs/atoms.fig/gas-base.gp
 create mode 100644 figs/atoms.fig/gas-rods-base.gp
 create mode 100644 figs/atoms.fig/gas-rods.py
 create mode 100644 figs/atoms.fig/gas.py
 create mode 100644 figs/atoms.fig/liquid-base.gp
 create mode 100644 figs/atoms.fig/liquid.py
 create mode 100644 figs/atoms.fig/nematic-base.gp
 create mode 100644 figs/atoms.fig/nematic.py
 create mode 100644 figs/atoms.fig/smectic-base.gp
 create mode 100644 figs/atoms.fig/smectic.py
 create mode 100644 figs/diamonds.fig/Makefile
 create mode 100644 figs/diamonds.fig/diamonds.py
 create mode 120000 figs/diamonds.fig/shapes.sty
 create mode 100644 figs/libs/shapes.sty
 create mode 100644 figs/rods.fig/Makefile
 create mode 120000 figs/rods.fig/libs/shapes.sty
 create mode 100644 figs/rods.fig/rods.tikz.tex
 create mode 100644 figs/shapes.fig/L_tetromino.tikz.tex
 create mode 100644 figs/shapes.fig/Makefile
 create mode 100644 figs/shapes.fig/P_pentomino.tikz.tex
 create mode 100644 figs/shapes.fig/T_tetromino.tikz.tex
 create mode 100644 figs/shapes.fig/V_triomino.tikz.tex
 create mode 100644 figs/shapes.fig/cross.tikz.tex
 create mode 100644 figs/shapes.fig/diamond.tikz.tex
 create mode 100644 figs/shapes.fig/hexagon.tikz.tex
 create mode 120000 figs/shapes.fig/libs/shapes.sty

(limited to 'figs')

diff --git a/figs/atoms.fig/Makefile b/figs/atoms.fig/Makefile
new file mode 100644
index 0000000..50559fa
--- /dev/null
+++ b/figs/atoms.fig/Makefile
@@ -0,0 +1,15 @@
+PROJECTNAME=crystal liquid gas nematic smectic gas-rods
+PNGS=$(addsuffix .png, $(PROJECTNAME))
+
+all: $(PNGS)
+
+$(PNGS):
+	cp $(patsubst %.png, %, $@)-base.gp $(patsubst %.png, %, $@).gp
+	python $(patsubst %.png, %, $@).py >> $(patsubst %.png, %, $@).gp
+	gnuplot $(patsubst %.png, %, $@).gp > $@
+
+clean-aux:
+	rm -f $(addsuffix .gp, $(PROJECTNAME))
+
+clean: clean-aux
+	rm -f $(PNGS)
diff --git a/figs/atoms.fig/crystal-base.gp b/figs/atoms.fig/crystal-base.gp
new file mode 100644
index 0000000..4de0ee2
--- /dev/null
+++ b/figs/atoms.fig/crystal-base.gp
@@ -0,0 +1,21 @@
+set terminal pngcairo size 2048,2048
+
+set key off
+unset colorbox
+unset border
+unset xtics
+unset ytics
+unset ztics
+
+set parametric
+
+set view equal xyz
+
+set isosample 100
+
+set pm3d depthorder
+set pm3d lighting primary 0.50 specular 0.6
+
+set palette defined (0 "#339999", 1 "#339999")
+
+splot \
diff --git a/figs/atoms.fig/crystal.py b/figs/atoms.fig/crystal.py
new file mode 100644
index 0000000..4b1ba3c
--- /dev/null
+++ b/figs/atoms.fig/crystal.py
@@ -0,0 +1,24 @@
+#!/usr/bin/env python3
+
+from math import *
+import random
+import sys
+
+# size of lattice
+N=5
+
+# configuration
+config=[]
+for i in range(N):
+    for j in range(N):
+        for k in range(N):
+            config.append([2*i+((j+k)%2),sqrt(3)*(j+(k%2)/3),2*sqrt(6)/3*k])
+
+
+for i in range(len(config)):
+    print(str(config[i][0])+"+cos(u)*sin(v)", end=",")
+    print(str(config[i][1])+"+sin(u)*sin(v)", end=",")
+    print(str(config[i][2])+"+cos(v)", end=" ")
+    print("with pm3d", end="")
+    if i<len(config)-1:
+        print(", \\")
diff --git a/figs/atoms.fig/gas-base.gp b/figs/atoms.fig/gas-base.gp
new file mode 100644
index 0000000..e95f005
--- /dev/null
+++ b/figs/atoms.fig/gas-base.gp
@@ -0,0 +1,21 @@
+set terminal pngcairo size 2048,2048
+
+set key off
+unset colorbox
+unset border
+unset xtics
+unset ytics
+unset ztics
+
+set parametric
+
+set view equal xyz
+
+set isosample 100
+
+set pm3d depthorder
+set pm3d lighting primary 0.5 specular 0.6
+
+set palette defined (0 "#339999", 1 "#339999")
+
+splot \
diff --git a/figs/atoms.fig/gas-rods-base.gp b/figs/atoms.fig/gas-rods-base.gp
new file mode 100644
index 0000000..4de0ee2
--- /dev/null
+++ b/figs/atoms.fig/gas-rods-base.gp
@@ -0,0 +1,21 @@
+set terminal pngcairo size 2048,2048
+
+set key off
+unset colorbox
+unset border
+unset xtics
+unset ytics
+unset ztics
+
+set parametric
+
+set view equal xyz
+
+set isosample 100
+
+set pm3d depthorder
+set pm3d lighting primary 0.50 specular 0.6
+
+set palette defined (0 "#339999", 1 "#339999")
+
+splot \
diff --git a/figs/atoms.fig/gas-rods.py b/figs/atoms.fig/gas-rods.py
new file mode 100644
index 0000000..dc63d24
--- /dev/null
+++ b/figs/atoms.fig/gas-rods.py
@@ -0,0 +1,88 @@
+#!/usr/bin/env python3
+
+from math import *
+import random
+
+# size of space
+L=30
+# number of rods
+N=15
+# aspect ratio
+a=10
+
+# check whether two rods overlap
+def check_overlap(rod1,rod2):
+    # relative placement
+    relative_pos=unrotate(subtract(rod2[0],rod1[0]), rod1[1])
+    if(abs(relative_pos[0])<2 and abs(relative_pos[1])<2 and abs(relative_pos[2])<2):
+        return(True)
+    # relative angle
+    relative_ang=cart_to_spherical(unrotate(spherical_to_cart(rod2[1]), rod1[1]))
+    # exclusion volume
+    # rotate other rod
+    relative_pos=unrotate(relative_pos, [0,relative_ang[1]])
+    #if(abs(relative_pos[1])<2 and abs(relative_pos[0])-2<abs(sin(relative_ang[0]))*a and abs(relative_pos[2])-a-2<abs(cos(relative_ang[0])*a)):
+    if(abs(relative_pos[1])<2 and abs(relative_pos[0])-2<abs(sin(relative_ang[0]))*a and abs(sin(relative_ang[0])*relative_pos[2]-cos(relative_ang[0])*relative_pos[0])-2<abs(sin(relative_ang[0])*a)):
+        return(True)
+    return(False)
+
+# def subtract vectors
+def subtract(x,y):
+    return([x[0]-y[0],x[1]-y[1],x[2]-y[2]])
+# rotate vector
+def unrotate(x,w):
+    ret=[x[0],x[1],x[2]]
+    # rotate phi
+    tmp=cos(w[1])*ret[0]+sin(w[1])*ret[1]
+    ret[1]=-sin(w[1])*ret[0]+cos(w[1])*ret[1]
+    ret[0]=tmp
+    # rotate theta
+    tmp=cos(w[0])*ret[0]-sin(w[0])*ret[2]
+    ret[2]=sin(w[0])*ret[0]+cos(w[0])*ret[2]
+    ret[0]=tmp
+    return(ret)
+
+# convert coordinates
+def spherical_to_cart(w):
+    return([cos(w[1])*sin(w[0]),sin(w[1])*sin(w[0]),cos(w[0])])
+def cart_to_spherical(x):
+    w=[0,0]
+    w[0]=acos(x[2])
+    if(sin(w[0]==0)):
+        return([w[0],0])
+    c=x[0]/sin(w[0])
+    s=x[1]/sin(w[0])
+    # to avoid truncation errors
+    if(abs(c)>1 and abs(c)<1.0001):
+        if(c>0):
+            return([w[0],0])
+        else:
+            return([w[0],pi])
+    if(s>=0):
+        return([w[0],acos(c)])
+    return([w[0],2*pi-acos(c)])
+
+# configuration
+config=[]
+# add rods
+while len(config)<N:
+    # random position and angles
+    x=[random.uniform(0,L), random.uniform(0,L), random.uniform(0,L)]
+    w=[random.uniform(0,pi), random.uniform(0,2*pi)]
+    # chek it does not interfere with other rods
+    fine=True
+    for rod in config:
+        if(check_overlap(rod,[x,w])):
+            fine=False
+            break
+    if fine:
+        config.append([x,w])
+
+for i in range(len(config)):
+    rod=config[i]
+    print(str(rod[0][0])+"+("+str(cos(rod[1][1])*cos(rod[1][0]))+")*cos(u)*sin(v)+("+str(-sin(rod[1][1]))+")*sin(u)*sin(v)+("+str(cos(rod[1][1])*sin(rod[1][0])*a)+")*cos(v)", end=", ")
+    print(str(rod[0][1])+"+("+str(sin(rod[1][1])*cos(rod[1][0]))+")*cos(u)*sin(v)+("+str(cos(rod[1][1]))+")*sin(u)*sin(v)+("+str(sin(rod[1][1])*sin(rod[1][0])*a)+")*cos(v)", end=", ")
+    print(str(rod[0][2])+"+("+str(-sin(rod[1][0]))+")*cos(u)*sin(v)+("+str(cos(rod[1][0])*a)+")*cos(v)", end="  ")
+    print("with pm3d", end="")
+    if i<len(config)-1:
+        print(", \\")
diff --git a/figs/atoms.fig/gas.py b/figs/atoms.fig/gas.py
new file mode 100644
index 0000000..8685999
--- /dev/null
+++ b/figs/atoms.fig/gas.py
@@ -0,0 +1,39 @@
+#!/usr/bin/env python3
+
+from math import *
+import random
+
+# size of space
+L=15
+# number of particles
+N=10
+
+# check whether two rods overlap
+def check_overlap(sphere1,sphere2):
+    if(sqrt((sphere2[0]-sphere1[0])**2+(sphere2[1]-sphere1[1])**2+(sphere2[2]-sphere1[2])**2)<2):
+        return(True)
+    return(False)
+
+# configuration
+config=[]
+# add spheres
+while len(config)<N:
+    # random position
+    x=[random.uniform(0,L), random.uniform(0,L), random.uniform(0,L)]
+    # check it does not interfere with other spheres
+    fine=True
+    for sphere in config:
+        if(check_overlap(sphere,x)):
+            fine=False
+            break
+    if fine:
+        config.append(x)
+
+for i in range(len(config)):
+    sphere=config[i]
+    print(str(sphere[0])+"+cos(u)*sin(v)", end=", ")
+    print(str(sphere[1])+"+sin(u)*sin(v)", end=", ")
+    print(str(sphere[2])+"+cos(v)", end="  ")
+    print("with pm3d", end="")
+    if i<len(config)-1:
+        print(", \\")
diff --git a/figs/atoms.fig/liquid-base.gp b/figs/atoms.fig/liquid-base.gp
new file mode 100644
index 0000000..4de0ee2
--- /dev/null
+++ b/figs/atoms.fig/liquid-base.gp
@@ -0,0 +1,21 @@
+set terminal pngcairo size 2048,2048
+
+set key off
+unset colorbox
+unset border
+unset xtics
+unset ytics
+unset ztics
+
+set parametric
+
+set view equal xyz
+
+set isosample 100
+
+set pm3d depthorder
+set pm3d lighting primary 0.50 specular 0.6
+
+set palette defined (0 "#339999", 1 "#339999")
+
+splot \
diff --git a/figs/atoms.fig/liquid.py b/figs/atoms.fig/liquid.py
new file mode 100644
index 0000000..99b09ba
--- /dev/null
+++ b/figs/atoms.fig/liquid.py
@@ -0,0 +1,39 @@
+#!/usr/bin/env python3
+
+from math import *
+import random
+
+# size of space
+L=15
+# number of particles
+N=100
+
+# check whether two rods overlap
+def check_overlap(sphere1,sphere2):
+    if(sqrt((sphere2[0]-sphere1[0])**2+(sphere2[1]-sphere1[1])**2+(sphere2[2]-sphere1[2])**2)<2):
+        return(True)
+    return(False)
+
+# configuration
+config=[]
+# add spheres
+while len(config)<N:
+    # random position
+    x=[random.uniform(0,L), random.uniform(0,L), random.uniform(0,L)]
+    # check it does not interfere with other spheres
+    fine=True
+    for sphere in config:
+        if(check_overlap(sphere,x)):
+            fine=False
+            break
+    if fine:
+        config.append(x)
+
+for i in range(len(config)):
+    sphere=config[i]
+    print(str(sphere[0])+"+cos(u)*sin(v)", end=", ")
+    print(str(sphere[1])+"+sin(u)*sin(v)", end=", ")
+    print(str(sphere[2])+"+cos(v)", end="  ")
+    print("with pm3d", end="")
+    if i<len(config)-1:
+        print(", \\")
diff --git a/figs/atoms.fig/nematic-base.gp b/figs/atoms.fig/nematic-base.gp
new file mode 100644
index 0000000..4de0ee2
--- /dev/null
+++ b/figs/atoms.fig/nematic-base.gp
@@ -0,0 +1,21 @@
+set terminal pngcairo size 2048,2048
+
+set key off
+unset colorbox
+unset border
+unset xtics
+unset ytics
+unset ztics
+
+set parametric
+
+set view equal xyz
+
+set isosample 100
+
+set pm3d depthorder
+set pm3d lighting primary 0.50 specular 0.6
+
+set palette defined (0 "#339999", 1 "#339999")
+
+splot \
diff --git a/figs/atoms.fig/nematic.py b/figs/atoms.fig/nematic.py
new file mode 100644
index 0000000..5c779c0
--- /dev/null
+++ b/figs/atoms.fig/nematic.py
@@ -0,0 +1,90 @@
+#!/usr/bin/env python3
+
+from math import *
+import random
+
+# size of space
+L=30
+# number of rods
+N=75
+# aspect ratio
+a=10
+# spread in theta angle
+spread=pi/30
+
+# check whether two rods overlap
+def check_overlap(rod1,rod2):
+    # relative placement
+    relative_pos=unrotate(subtract(rod2[0],rod1[0]), rod1[1])
+    if(abs(relative_pos[0])<2 and abs(relative_pos[1])<2 and abs(relative_pos[2])<2):
+        return(True)
+    # relative angle
+    relative_ang=cart_to_spherical(unrotate(spherical_to_cart(rod2[1]), rod1[1]))
+    # exclusion volume
+    # rotate other rod
+    relative_pos=unrotate(relative_pos, [0,relative_ang[1]])
+    #if(abs(relative_pos[1])<2 and abs(relative_pos[0])-2<abs(sin(relative_ang[0]))*a and abs(relative_pos[2])-a-2<abs(cos(relative_ang[0])*a)):
+    if(abs(relative_pos[1])<2 and abs(relative_pos[0])-2<abs(sin(relative_ang[0]))*a and abs(sin(relative_ang[0])*relative_pos[2]-cos(relative_ang[0])*relative_pos[0])-2<abs(sin(relative_ang[0])*a)):
+        return(True)
+    return(False)
+
+# def subtract vectors
+def subtract(x,y):
+    return([x[0]-y[0],x[1]-y[1],x[2]-y[2]])
+# rotate vector
+def unrotate(x,w):
+    ret=[x[0],x[1],x[2]]
+    # rotate phi
+    tmp=cos(w[1])*ret[0]+sin(w[1])*ret[1]
+    ret[1]=-sin(w[1])*ret[0]+cos(w[1])*ret[1]
+    ret[0]=tmp
+    # rotate theta
+    tmp=cos(w[0])*ret[0]-sin(w[0])*ret[2]
+    ret[2]=sin(w[0])*ret[0]+cos(w[0])*ret[2]
+    ret[0]=tmp
+    return(ret)
+
+# convert coordinates
+def spherical_to_cart(w):
+    return([cos(w[1])*sin(w[0]),sin(w[1])*sin(w[0]),cos(w[0])])
+def cart_to_spherical(x):
+    w=[0,0]
+    w[0]=acos(x[2])
+    if(sin(w[0]==0)):
+        return([w[0],0])
+    c=x[0]/sin(w[0])
+    s=x[1]/sin(w[0])
+    # to avoid truncation errors
+    if(abs(c)>1 and abs(c)<1.0001):
+        if(c>0):
+            return([w[0],0])
+        else:
+            return([w[0],pi])
+    if(s>=0):
+        return([w[0],acos(c)])
+    return([w[0],2*pi-acos(c)])
+
+# configuration
+config=[]
+# add rods
+while len(config)<N:
+    # random position and angles
+    x=[random.uniform(0,L), random.uniform(0,L), random.uniform(0,L)]
+    w=[abs(random.gauss(0,spread)), random.uniform(0,2*pi)]
+    # chek it does not interfere with other rods
+    fine=True
+    for rod in config:
+        if(check_overlap(rod,[x,w])):
+            fine=False
+            break
+    if fine:
+        config.append([x,w])
+
+for i in range(len(config)):
+    rod=config[i]
+    print(str(rod[0][0])+"+("+str(cos(rod[1][1])*cos(rod[1][0]))+")*cos(u)*sin(v)+("+str(-sin(rod[1][1]))+")*sin(u)*sin(v)+("+str(cos(rod[1][1])*sin(rod[1][0])*a)+")*cos(v)", end=", ")
+    print(str(rod[0][1])+"+("+str(sin(rod[1][1])*cos(rod[1][0]))+")*cos(u)*sin(v)+("+str(cos(rod[1][1]))+")*sin(u)*sin(v)+("+str(sin(rod[1][1])*sin(rod[1][0])*a)+")*cos(v)", end=", ")
+    print(str(rod[0][2])+"+("+str(-sin(rod[1][0]))+")*cos(u)*sin(v)+("+str(cos(rod[1][0])*a)+")*cos(v)", end="  ")
+    print("with pm3d", end="")
+    if i<len(config)-1:
+        print(", \\")
diff --git a/figs/atoms.fig/smectic-base.gp b/figs/atoms.fig/smectic-base.gp
new file mode 100644
index 0000000..6b2077f
--- /dev/null
+++ b/figs/atoms.fig/smectic-base.gp
@@ -0,0 +1,21 @@
+set terminal pngcairo size 2048,2048
+
+set key off
+unset colorbox
+unset border
+unset xtics
+unset ytics
+unset ztics
+
+set parametric
+
+set view 90,0
+
+set isosample 100
+
+set pm3d depthorder
+set pm3d lighting primary 0.50 specular 0.6
+
+set palette defined (0 "#339999", 1 "#339999")
+
+splot \
diff --git a/figs/atoms.fig/smectic.py b/figs/atoms.fig/smectic.py
new file mode 100644
index 0000000..c8d4d13
--- /dev/null
+++ b/figs/atoms.fig/smectic.py
@@ -0,0 +1,92 @@
+#!/usr/bin/env python3
+
+from math import *
+import random
+
+# size of space
+L=30
+# number of rods
+N=150
+# aspect ratio
+a=10
+# spread in theta angle
+spread=pi/30
+# spread in height
+spread_height=a/5
+
+# check whether two rods overlap
+def check_overlap(rod1,rod2):
+    # relative placement
+    relative_pos=unrotate(subtract(rod2[0],rod1[0]), rod1[1])
+    if(abs(relative_pos[0])<2 and abs(relative_pos[1])<2 and abs(relative_pos[2])<2):
+        return(True)
+    # relative angle
+    relative_ang=cart_to_spherical(unrotate(spherical_to_cart(rod2[1]), rod1[1]))
+    # exclusion volume
+    # rotate other rod
+    relative_pos=unrotate(relative_pos, [0,relative_ang[1]])
+    #if(abs(relative_pos[1])<2 and abs(relative_pos[0])-2<abs(sin(relative_ang[0]))*a and abs(relative_pos[2])-a-2<abs(cos(relative_ang[0])*a)):
+    if(abs(relative_pos[1])<2 and abs(relative_pos[0])-2<abs(sin(relative_ang[0]))*a and abs(sin(relative_ang[0])*relative_pos[2]-cos(relative_ang[0])*relative_pos[0])-2<abs(sin(relative_ang[0])*a)):
+        return(True)
+    return(False)
+
+# def subtract vectors
+def subtract(x,y):
+    return([x[0]-y[0],x[1]-y[1],x[2]-y[2]])
+# rotate vector
+def unrotate(x,w):
+    ret=[x[0],x[1],x[2]]
+    # rotate phi
+    tmp=cos(w[1])*ret[0]+sin(w[1])*ret[1]
+    ret[1]=-sin(w[1])*ret[0]+cos(w[1])*ret[1]
+    ret[0]=tmp
+    # rotate theta
+    tmp=cos(w[0])*ret[0]-sin(w[0])*ret[2]
+    ret[2]=sin(w[0])*ret[0]+cos(w[0])*ret[2]
+    ret[0]=tmp
+    return(ret)
+
+# convert coordinates
+def spherical_to_cart(w):
+    return([cos(w[1])*sin(w[0]),sin(w[1])*sin(w[0]),cos(w[0])])
+def cart_to_spherical(x):
+    w=[0,0]
+    w[0]=acos(x[2])
+    if(sin(w[0]==0)):
+        return([w[0],0])
+    c=x[0]/sin(w[0])
+    s=x[1]/sin(w[0])
+    # to avoid truncation errors
+    if(abs(c)>1 and abs(c)<1.0001):
+        if(c>0):
+            return([w[0],0])
+        else:
+            return([w[0],pi])
+    if(s>=0):
+        return([w[0],acos(c)])
+    return([w[0],2*pi-acos(c)])
+
+# configuration
+config=[]
+# add rods
+while len(config)<N:
+    # random position and angles
+    x=[random.uniform(0,L), random.uniform(0,L), 1.6*a*random.randint(0,2)+random.gauss(0,spread_height)]
+    w=[abs(random.gauss(0,spread)), random.uniform(0,2*pi)]
+    # chek it does not interfere with other rods
+    fine=True
+    for rod in config:
+        if(check_overlap(rod,[x,w])):
+            fine=False
+            break
+    if fine:
+        config.append([x,w])
+
+for i in range(len(config)):
+    rod=config[i]
+    print(str(rod[0][0])+"+("+str(cos(rod[1][1])*cos(rod[1][0]))+")*cos(u)*sin(v)+("+str(-sin(rod[1][1]))+")*sin(u)*sin(v)+("+str(cos(rod[1][1])*sin(rod[1][0])*a)+")*cos(v)", end=", ")
+    print(str(rod[0][1])+"+("+str(sin(rod[1][1])*cos(rod[1][0]))+")*cos(u)*sin(v)+("+str(cos(rod[1][1]))+")*sin(u)*sin(v)+("+str(sin(rod[1][1])*sin(rod[1][0])*a)+")*cos(v)", end=", ")
+    print(str(rod[0][2])+"+("+str(-sin(rod[1][0]))+")*cos(u)*sin(v)+("+str(cos(rod[1][0])*a)+")*cos(v)", end="  ")
+    print("with pm3d", end="")
+    if i<len(config)-1:
+        print(", \\")
diff --git a/figs/diamonds.fig/Makefile b/figs/diamonds.fig/Makefile
new file mode 100644
index 0000000..42b4031
--- /dev/null
+++ b/figs/diamonds.fig/Makefile
@@ -0,0 +1,20 @@
+all: diamonds
+
+diamonds:
+	python diamonds.py > diamonds.tikz.tex
+	cat diamonds.tikz.tex | sed 's/%1%/red/g;s/%2%/blue/g' > diamonds_color.tikz.tex
+	sed -i 's/%1%/teal/g;s/%2%/teal/g' diamonds.tikz.tex
+	pdflatex -jobname diamonds diamonds.tikz.tex
+	pdflatex -jobname diamonds_color diamonds_color.tikz.tex
+
+clean-aux:
+	rm -f diamonds.tikz.tex
+	rm -f diamonds.log
+	rm -f diamonds.aux
+	rm -f diamonds_color.tikz.tex
+	rm -f diamonds_color.log
+	rm -f diamonds_color.aux
+
+clean: clean-aux
+	rm -f diamonds.pdf
+	rm -f diamonds_color.pdf
diff --git a/figs/diamonds.fig/diamonds.py b/figs/diamonds.fig/diamonds.py
new file mode 100644
index 0000000..2bc4d9c
--- /dev/null
+++ b/figs/diamonds.fig/diamonds.py
@@ -0,0 +1,65 @@
+#!/usr/bin/env python3
+
+from math import *
+import random
+
+# size of space (must be int)
+L=30
+# number of particles
+N=int(L*L/2*0.97)
+
+# check whether two diamonds overlap
+def check_overlap(x1,x2):
+    if(sqrt((x1[0]-x2[0])**2+(x1[1]-x2[1])**2)<=1):
+        return(True)
+    return(False)
+
+# configuration
+config=[]
+
+# put particles on odd lattice manually
+for i in range(4):
+    for j in range(4):
+        if (i!=2 or j!=1):
+            config.append([2*int(L/2/2)+1+i+j,2*int(L/2/2)+i-j])
+
+# add particles
+while len(config)<N:
+    # random position
+    # even sublattice
+    if(random.random()<0.5):
+        x=[2*random.randint(0,int(L/2)), 2*random.randint(0,int(L/2))]
+    else:
+        x=[2*random.randint(0,int(L/2))+1, 2*random.randint(0,int(L/2))+1]
+    # check it does not interfere with other particles
+    fine=True
+    for part in config:
+        if(check_overlap(part,x)):
+            fine=False
+            break
+    if fine:
+        config.append(x)
+
+print(r'''\documentclass{standalone}
+\usepackage{tikz}
+\usepackage{shapes}
+
+\begin{document}
+\begin{tikzpicture}
+\grid{'''+str(L+3)+'}{'+str(L+3)+'''}{(-1,-1)}
+''')
+
+for i in range(len(config)):
+    part=config[i]
+    # different colors for even and odd
+    if i<15:
+        # replace %1% later
+        print(r'\diamond{%1%}{('+str(part[0])+','+str(part[1])+')}')
+    else:
+        # replace %2% later
+        print(r'\diamond{%2%}{('+str(part[0])+','+str(part[1])+')}')
+
+print(r'''
+\end{tikzpicture}
+\end{document}
+''')
diff --git a/figs/diamonds.fig/shapes.sty b/figs/diamonds.fig/shapes.sty
new file mode 120000
index 0000000..2607bef
--- /dev/null
+++ b/figs/diamonds.fig/shapes.sty
@@ -0,0 +1 @@
+../libs/shapes.sty
\ No newline at end of file
diff --git a/figs/libs/shapes.sty b/figs/libs/shapes.sty
new file mode 100644
index 0000000..e60faeb
--- /dev/null
+++ b/figs/libs/shapes.sty
@@ -0,0 +1,109 @@
+% 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);
+  }
+}
+
+
+% cross (color #1, position #2)
+\def\cross#1#2{
+  \fill[color=#1]#2++(0.5,0.5)--++(0,1)--++(-1,0)--++(0,-1)--++(-1,0)--++(0,-1)--++(1,0)--++(0,-1)--++(1,0)--++(0,1)--++(1,0)--++(0,1)--++(-1,0);
+  \begin{scope}
+    \clip#2++(0.5,0.5)--++(0,1)--++(-1,0)--++(0,-1)--++(-1,0)--++(0,-1)--++(1,0)--++(0,-1)--++(1,0)--++(0,1)--++(1,0)--++(0,1)--++(-1,0);
+    \grid44{[color=white]#2++(-2,-2)}
+  \end{scope}
+  \draw[color=black]#2++(0.5,0.5)--++(0,1)--++(-1,0)--++(0,-1)--++(-1,0)--++(0,-1)--++(1,0)--++(0,-1)--++(1,0)--++(0,1)--++(1,0)--++(0,1)--++(-1,0);
+}
+
+% V triomino (color #1, position #2)
+\def\Vtriomino#1#2{
+  \fill[color=#1]#2++(0.5,0.5)--++(0,1)--++(-1,0)--++(0,-2)--++(2,0)--++(0,1)--++(-1,0);
+  \begin{scope}
+    \clip#2++(0.5,0.5)--++(0,1)--++(-1,0)--++(0,-2)--++(2,0)--++(0,1)--++(-1,0);
+    \grid33{[color=white]#2++(-1,-1)}
+  \end{scope}
+  \draw[color=black]#2++(0.5,0.5)--++(0,1)--++(-1,0)--++(0,-2)--++(2,0)--++(0,1)--++(-1,0);
+}
+
+% T tetromino (color #1, position #2)
+\def\Ttetromino#1#2{
+  \fill[color=#1]#2++(0.5,0.5)--++(0,1)--++(-1,0)--++(0,-3)--++(1,0)--++(0,1)--++(1,0)--++(0,1)--++(-1,0);
+  \begin{scope}
+    \clip#2++(0.5,0.5)--++(0,1)--++(-1,0)--++(0,-3)--++(1,0)--++(0,1)--++(1,0)--++(0,1)--++(-1,0);
+    \grid34{[color=white]#2++(-1,-2)}
+  \end{scope}
+  \draw[color=black]#2++(0.5,0.5)--++(0,1)--++(-1,0)--++(0,-3)--++(1,0)--++(0,1)--++(1,0)--++(0,1)--++(-1,0);
+}
+
+% L tetromino (color #1, position #2)
+\def\Ltetromino#1#2{
+  \fill[color=#1]#2++(0.5,0.5)--++(0,1)--++(-1,0)--++(0,-3)--++(2,0)--++(0,1)--++(-1,0)--++(0,1);
+  \begin{scope}
+    \clip#2++(0.5,0.5)--++(0,1)--++(-1,0)--++(0,-3)--++(2,0)--++(0,1)--++(-1,0)--++(0,1);
+    \grid34{[color=white]#2++(-1,-2)}
+  \end{scope}
+  \draw[color=black]#2++(0.5,0.5)--++(0,1)--++(-1,0)--++(0,-3)--++(2,0)--++(0,1)--++(-1,0)--++(0,1);
+}
+
+% P pentomino (color #1, position #2)
+\def\Ppentomino#1#2{
+  \fill[color=#1]#2++(1.5,1.5)--++(-2,0)--++(0,-3)--++(1,0)--++(0,1)--++(1,0)--++(0,2);
+  \begin{scope}
+    \clip#2++(1.5,1.5)--++(-2,0)--++(0,-3)--++(1,0)--++(0,1)--++(1,0)--++(0,2);
+    \grid34{[color=white]#2++(-1,-2)}
+  \end{scope}
+  \draw[color=black]#2++(1.5,1.5)--++(-2,0)--++(0,-3)--++(1,0)--++(0,1)--++(1,0)--++(0,2);
+}
+
+% 1x1 square (color #1, position #2)
+\def\square#1#2{
+  \fill[color=#1]#2++(-0.5,-0.5)--++(0,1)--++(1,0)--++(0,-1)--cycle;
+  \draw[color=black]#2++(-0.5,-0.5)--++(0,1)--++(1,0)--++(0,-1)--cycle;
+  \draw[color=white]#2++(-0.5,0)--++(1,0);
+  \draw[color=white]#2++(0,-0.5)--++(0,1);
+}
+
+% 2x2 square (color #1, position #2)
+\def\ttsquare#1#2{
+  \fill[color=#1]#2++(-1,-1)--++(0,2)--++(2,0)--++(0,-2)--cycle;
+  \draw[color=black]#2++(-1,-1)--++(0,2)--++(2,0)--++(0,-2)--cycle;
+  \draw[color=white]#2++(-0.5,-1)--++(0,2);
+  \draw[color=white]#2++(0.5,-1)--++(0,2);
+  \draw[color=white]#2++(-1,-0.5)--++(2,0);
+  \draw[color=white]#2++(-1,0.5)--++(2,0);
+}
+\def\ttsquareempty#1{
+  \draw[color=black]#1++(-1,-1)--++(0,2)--++(2,0)--++(0,-2)--cycle;
+}
+
+% diamond (color #1, position #2)
+\def\diamond#1#2{
+  \fill[color=#1]#2++(0,-1)--++(1,1)--++(-1,1)--++(-1,-1)--cycle;
+  \begin{scope}
+    \clip#2++(0,-1)--++(1,1)--++(-1,1)--++(-1,-1)--cycle;
+    \grid22{[color=white]#2++(-1,-1)}
+  \end{scope}
+  \draw[color=black]#2++(0,-1)--++(1,1)--++(-1,1)--++(-1,-1)--cycle;
+}
+
+% rods (color #1, position #2)
+\def\rodh#1#2{
+  \fill[color=#1]#2++(-5.5,-0.5)--++(11,0)--++(0,1)--++(-11,0)--cycle;
+  \begin{scope}
+    \clip#2++(-5.5,-0.5)--++(11,0)--++(0,1)--++(-11,0)--cycle;
+    \grid{12}2{[color=white]#2++(-6,-1)}
+  \end{scope}
+  \draw[color=black]#2++(-5.5,-0.5)--++(11,0)--++(0,1)--++(-11,0)--cycle;
+}
+\def\rodv#1#2{
+  \fill[color=#1]#2++(-0.5,-5.5)--++(0,11)--++(1,0)--++(0,-11)--cycle;
+  \begin{scope}
+    \clip#2++(-0.5,-5.5)--++(0,11)--++(1,0)--++(0,-11)--cycle;
+    \grid2{12}{[color=white]#2++(-1,-6)}
+  \end{scope}
+  \draw[color=black]#2++(-0.5,-5.5)--++(0,11)--++(1,0)--++(0,-11)--cycle;
+}
diff --git a/figs/rods.fig/Makefile b/figs/rods.fig/Makefile
new file mode 100644
index 0000000..33b81e2
--- /dev/null
+++ b/figs/rods.fig/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 $(PDFS)
+
+clean: clean-libs clean-aux clean-tex
diff --git a/figs/rods.fig/libs/shapes.sty b/figs/rods.fig/libs/shapes.sty
new file mode 120000
index 0000000..eaa25c7
--- /dev/null
+++ b/figs/rods.fig/libs/shapes.sty
@@ -0,0 +1 @@
+../../libs/shapes.sty
\ No newline at end of file
diff --git a/figs/rods.fig/rods.tikz.tex b/figs/rods.fig/rods.tikz.tex
new file mode 100644
index 0000000..935a72f
--- /dev/null
+++ b/figs/rods.fig/rods.tikz.tex
@@ -0,0 +1,30 @@
+\documentclass{standalone}
+
+\usepackage{tikz}
+\usepackage{shapes}
+
+\begin{document}
+\begin{tikzpicture}
+\grid{27}{27}{(-13,-13)}
+
+\rodh{teal}{(0,0)}
+\rodh{teal}{(2,1)}
+\rodh{teal}{(8,3)}
+\rodh{teal}{(-6,6)}
+\rodh{teal}{(8,6)}
+\rodh{teal}{(-7,7)}
+\rodh{teal}{(8,8)}
+\rodh{teal}{(-6,10)}
+\rodh{teal}{(-4,-2)}
+\rodh{teal}{(8,-2)}
+\rodh{teal}{(-1,-5)}
+\rodh{teal}{(-3,-7)}
+\rodh{teal}{(5,-8)}
+\rodh{teal}{(-3,-10)}
+
+\rodv{teal}{(-12,-1)}
+\rodv{teal}{(-11,-5)}
+\rodv{teal}{(1,8)}
+
+\end{tikzpicture}
+\end{document}
diff --git a/figs/shapes.fig/L_tetromino.tikz.tex b/figs/shapes.fig/L_tetromino.tikz.tex
new file mode 100644
index 0000000..5c82766
--- /dev/null
+++ b/figs/shapes.fig/L_tetromino.tikz.tex
@@ -0,0 +1,11 @@
+\documentclass{standalone}
+
+\usepackage{tikz}
+\usepackage{shapes}
+
+\begin{document}
+\begin{tikzpicture}
+\grid34{(-1,-2)}
+\Ltetromino{teal}{(0,0)}
+\end{tikzpicture}
+\end{document}
diff --git a/figs/shapes.fig/Makefile b/figs/shapes.fig/Makefile
new file mode 100644
index 0000000..33b81e2
--- /dev/null
+++ b/figs/shapes.fig/Makefile
@@ -0,0 +1,28 @@
+PROJECTNAME=$(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
diff --git a/figs/shapes.fig/P_pentomino.tikz.tex b/figs/shapes.fig/P_pentomino.tikz.tex
new file mode 100644
index 0000000..9ef3990
--- /dev/null
+++ b/figs/shapes.fig/P_pentomino.tikz.tex
@@ -0,0 +1,11 @@
+\documentclass{standalone}
+
+\usepackage{tikz}
+\usepackage{shapes}
+
+\begin{document}
+\begin{tikzpicture}
+\grid34{(-1,-2)}
+\Ppentomino{teal}{(0,0)}
+\end{tikzpicture}
+\end{document}
diff --git a/figs/shapes.fig/T_tetromino.tikz.tex b/figs/shapes.fig/T_tetromino.tikz.tex
new file mode 100644
index 0000000..087e809
--- /dev/null
+++ b/figs/shapes.fig/T_tetromino.tikz.tex
@@ -0,0 +1,11 @@
+\documentclass{standalone}
+
+\usepackage{tikz}
+\usepackage{shapes}
+
+\begin{document}
+\begin{tikzpicture}
+\grid34{(-1,-2)}
+\Ttetromino{teal}{(0,0)}
+\end{tikzpicture}
+\end{document}
diff --git a/figs/shapes.fig/V_triomino.tikz.tex b/figs/shapes.fig/V_triomino.tikz.tex
new file mode 100644
index 0000000..ba07c5f
--- /dev/null
+++ b/figs/shapes.fig/V_triomino.tikz.tex
@@ -0,0 +1,11 @@
+\documentclass{standalone}
+
+\usepackage{tikz}
+\usepackage{shapes}
+
+\begin{document}
+\begin{tikzpicture}
+\grid33{(-1,-1)}
+\Vtriomino{teal}{(0,0)}
+\end{tikzpicture}
+\end{document}
diff --git a/figs/shapes.fig/cross.tikz.tex b/figs/shapes.fig/cross.tikz.tex
new file mode 100644
index 0000000..ef5f391
--- /dev/null
+++ b/figs/shapes.fig/cross.tikz.tex
@@ -0,0 +1,11 @@
+\documentclass{standalone}
+
+\usepackage{tikz}
+\usepackage{shapes}
+
+\begin{document}
+\begin{tikzpicture}
+\grid44{(-2,-2)}
+\cross{teal}{(0,0)}
+\end{tikzpicture}
+\end{document}
diff --git a/figs/shapes.fig/diamond.tikz.tex b/figs/shapes.fig/diamond.tikz.tex
new file mode 100644
index 0000000..6d9eaa4
--- /dev/null
+++ b/figs/shapes.fig/diamond.tikz.tex
@@ -0,0 +1,11 @@
+\documentclass{standalone}
+
+\usepackage{tikz}
+\usepackage{shapes}
+
+\begin{document}
+\begin{tikzpicture}
+\grid44{(-2,-2)}
+\diamond{teal}{(0,0)}
+\end{tikzpicture}
+\end{document}
diff --git a/figs/shapes.fig/hexagon.tikz.tex b/figs/shapes.fig/hexagon.tikz.tex
new file mode 100644
index 0000000..a23b7dc
--- /dev/null
+++ b/figs/shapes.fig/hexagon.tikz.tex
@@ -0,0 +1,37 @@
+\documentclass{standalone}
+
+\usepackage{tikz}
+\usepackage{shapes}
+
+\begin{document}
+\begin{tikzpicture}
+
+\draw(0,0)--++(2,0);
+\draw(120:1)--++(3,0);
+\draw(120:2)--++(4,0);
+\draw(120:2)++(60:1)--++(3,0);
+\draw(120:2)++(60:2)--++(2,0);
+
+\draw(0,0)--++(60:4);
+\draw(1,0)--++(60:3);
+\draw(2,0)--++(60:2);
+\draw(120:1)--++(60:3);
+\draw(120:2)--++(60:2);
+
+\draw(0,0)--++(120:2);
+\draw(1,0)--++(120:3);
+\draw(2,0)--++(120:4);
+\draw(2,0)++(60:1)--++(120:3);
+\draw(2,0)++(60:2)--++(120:2);
+
+\fill[color=teal](60:1)--++(0:1)--++(60:1)--++(120:1)--++(180:1)--++(240:1)--++(300:1)--cycle;
+
+\draw[color=white](60:1)--++(60:2);
+\draw[color=white](60:1)++(1,0)--++(120:2);
+\draw[color=white](60:1)++(120:1)--++(2,0);
+
+\draw(60:1)--++(0:1)--++(60:1)--++(120:1)--++(180:1)--++(240:1)--++(300:1)--cycle;
+
+
+\end{tikzpicture}
+\end{document}
diff --git a/figs/shapes.fig/libs/shapes.sty b/figs/shapes.fig/libs/shapes.sty
new file mode 120000
index 0000000..eaa25c7
--- /dev/null
+++ b/figs/shapes.fig/libs/shapes.sty
@@ -0,0 +1 @@
+../../libs/shapes.sty
\ No newline at end of file
-- 
cgit v1.2.3-70-g09d2