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\documentclass[border=10pt]{standalone} \usepackage[inline]{asymptote} \begin{document} \begin{asy}[width=\the\linewidth,inline=true] pen lineAb=black+3pt; pen lineAt=white+1.2pt; pen lineB=dashed+darkblue+1.3pt; pen circA=lightyellow; pen circB=darkblue; pen rimA=red; pen rimB=blue; pen shade=springgreen; guide circ=unitcircle; real d=5; pair a,b,c,u; a=(0,-d); b=(d,-d); c=(d,0); u=1.618b; guide ga=shift(a.x,a.y)*circ; guide gc=shift(c.x,c.y)*circ; guide garc=a{dir(-45)}..u..{dir(135)}c; pair xa=intersectionpoint(ga,c–a); pair xc=intersectionpoint(gc,a–c);… Continue Reading →
This example plots a spiral of roots. \documentclass[border=10pt]{standalone} \usepackage[inline]{asymptote} \begin{document} \begin{asydef} unitsize(2cm); import fontsize; defaultpen(fontsize(9pt)); pen linepen=deepblue+0.8bp; pen labelpen=black; pen markpen=gray+0.6bp; void spiralOfRoots(int n){ assert(n>0); real w=0.15; pair O=0E,a=E,b; pair p,q,r; for(int i=1;i<=n;++i){ draw(O–a,linepen); label(“$\sqrt{“+string(i)+”}$”,O–a,O,labelpen,UnFill); b=a+dir(degrees(a)+90); draw(a–b,linepen); p= w*dir(b-a); r=-w*dir(a);… Continue Reading →
This example plots a lattice of points on the surface of a torus. \documentclass[border=10pt]{standalone} \usepackage[inline]{asymptote} \begin{document} \begin{asy}[width=\the\linewidth,inline=true] settings.outformat=”pdf”; settings.render=0; settings.prc=false; import graph3; pen surfPen=rgb(1,0.7,0); pen xarcPen=deepblue+0.7bp; pen yarcPen=deepred+0.7bp; currentprojection=perspective(5,4,4); real R=2; real a=1; triple fs(pair t) { return ((R+a*Cos(t.y))*Cos(t.x),(R+a*Cos(t.y))*Sin(t.x),a*Sin(t.y)); }… Continue Reading →
This solution illustrates (a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3. \documentclass[border=10pt]{standalone} \usepackage[inline]{asymptote} \begin{document} \begin{asy}[width=\the\linewidth,inline=true] settings.outformat=”pdf”; settings.render=0; settings.prc=false; unitsize(1cm); import three; currentprojection=orthographic(3,2,1,center=true,zoom=.8); //currentprojection=orthographic(0,10,0,zoom=.8); light White=light(new pen[] {rgb(0.38,0.38,0.45),rgb(0.6,0.6,0.67), rgb(0.5,0.5,0.57)},specularfactor=3, new triple[] {(5,5,5),(0,5,5),(-0.5,0,2)}); currentlight=White; real a=3.2, b=1.5; path3[] p=unitbox; surface q=unitcube;… Continue Reading →
A fish for fun \documentclass[border=10pt]{standalone} \usepackage[inline]{asymptote} \begin{document} \begin{asy}[width=\the\linewidth,inline=true] settings.outformat=”pdf”; settings.render=0; settings.prc=false; real w=600,h=400; size(h,w); pen bgPen=rgb(0,0.647,1), bodyPen=rgb(0.847,0.196,0.133), whitePen=rgb(1,1,1), eyePen=rgb(0.004,0.18,1)+opacity(0.01), mouthPen=rgb(1,1,1), scalesPen=rgb(0.98,1,0)+12pt; pair[][] bBody={ {(454,270),(436,252),(443,251),},{(433,269),(424,286),(398,322),}, {(361,352),(324,382),(276,405),},{(218,394),(160,382),(92,334),}, {(55,295),(18,256),(12,226),},{(13,187),(14,149),(21,102),}, {(65,66),(109,30),(189,3),},{(243,2),(296,1),(322,24),}, {(348,46),(374,68),(398,89),},{(414,109),(430,129),(437,149),}, {(450,143),(463,137),(481,105),},{(504,80),(526,55),(552,37),}, {(568,40),(585,43),(592,66),},{(584,97),(576,128),(553,166),}, {(542,181),(531,197),(531,189),},{(543,204),(555,218),(579,256),}, {(585,286),(591,316),(578,339),},{(571,349),(563,359),(561,356),}, {(538,338),(515,320),(472,287),}, }; pair[][] bWhite={ {(223,261),(227,278),(209,303),},{(192,312),(174,321),(156,315),}, {(141,304),(127,293),(115,276),},{(116,260),(118,244),(132,228),}, {(143,222),(155,215),(162,220),},{(179,227),(195,234),(220,244),}, };… Continue Reading →
The Möbius strip, as a parametric surface. \documentclass[border=10pt]{standalone} \usepackage[inline]{asymptote} \begin{document} \begin{asy}[width=\the\linewidth,inline=true] settings.outformat=”pdf”; settings.render=0; settings.prc=false; import graph3; size(200,IgnoreAspect); size3(200,IgnoreAspect); currentprojection=orthographic(camera=(1.5,0.3,2),up=Z,target=(0.5,0,0),zoom=0.8); real r=2, w=1; real x(real u, real v){return (r+v/2*cos(3pi*u))*cos(2pi*u);}; real y(real u, real v){return (r+v/2*cos(3pi*u))*sin(2pi*u);}; real z(real u, real v){return (v/2*sin(3pi*u));};… Continue Reading →
\documentclass[border=10pt]{standalone} \usepackage{asymptote} \begin{document} \begin{asy}[width=\the\linewidth,inline=true] settings.outformat=”pdf”; settings.render=0; settings.prc=false; import graph3; import tube; size(200,0); currentlight.background=paleyellow+opacity(0.0); currentprojection=orthographic(camera=(-40,9,70), up=Z); real x(real t){return sin(t)+2sin(2t);} real y(real t){return cos(t)-2cos(2t);} real z(real t){return -sin(3t);} guide3 g=graph(x,y,z, 0, 2pi,operator..); draw(tube(g,circle((0,0),0.618)),white); \end{asy} \end{document} Source: TeX.SE Author: g.kov (License) See… Continue Reading →
\documentclass[border=10pt]{standalone} \usepackage{asymptote} \begin{document} \begin{asy}[width=\the\linewidth,inline=true] settings.outformat=”pdf”; settings.render=0; settings.prc=false; import graph3; import tube; size(200,0); currentlight.background=paleyellow+opacity(0.0); currentprojection=orthographic(camera=(-10,49,-58),up=(0.92,0.36,0.14)); real x(real t){return sin(2pi*t)+2sin(2*2pi*t);} real y(real t){return cos(2pi*t)-2cos(2*2pi*t);} real z(real t){return -sin(3*2pi*t);} guide3 g=graph(x,y,z, 0, 1,operator..); pair[][] p={ {(-40, 20),( -56.8421, 23.4210),( -78.9473, 28.6842),(-90, 20)}, {(-90,… Continue Reading →
The following image illustrates the blowup of a plane at a point–an important construction in algebraic geometry. \documentclass[border=10pt]{standalone} \usepackage[inline]{asymptote} \begin{document} \begin{asy}[width=\the\linewidth,inline=true] settings.outformat=”pdf”; settings.render=0; settings.prc=false; usepackage(“lmodern”); usepackage(“fontenc”,”T1″); usepackage(“amssymb”); // for the \mathbb command defaultpen(fontsize(10pt)); import graph3; size(400,400); currentprojection=orthographic(5,-10,4); real R=8; struct… Continue Reading →
\documentclass[border=10pt]{standalone} \usepackage{asymptote} \begin{document} \begin{asy}[width=\the\linewidth,inline=true] settings.outformat=”pdf”; settings.render=0; settings.prc=false; size(7cm); import fontsize; defaultpen(fontsize(9pt)); real wd=0.6bp; pen dotPen=deepblue+wd; pen dotFill=dotPen; pen dotPenB=blue+wd; pen dotPenC=red+wd; pen linePen=deepblue+wd; pen fillPen=lightgreen+opacity(0.5); pen thinLinePen=black+wd/2; guide[] g; g=texpath(“$\Omega$”); filldraw(g,fillPen,linePen); pair a,b,c,d; pair labdir; int pointNo=0; for(int i=0;i<g.length;++i){ for(int… Continue Reading →
\documentclass[margin=10pt,convert]{standalone} \usepackage{asymptote} \begin{document} \begin{asydef} // Global Asymptote definitions real linkLen=1, linkWidth=2pt; real rl=2+linkLen; // distance between beads guide link=(1,0)–(1+linkLen,0); // a link pen beadColor=orange; pen linkColor=beadColor; void bead(transform t){ draw(t*link,linkColor+linkWidth); radialshade(t*unitcircle, beadColor,shift(t)*(-0.4,0.3),0.01 ,black,shift(t)*(-0.4,0.3),1.5); } pair operator>(pair pos=(0,0), real phi){ transform… Continue Reading →
Some leading-order diagrams of basic QCD processes, inspired by Table 7.1 of Griffith’s Introduction to Elementary Particles (2008). Electron-muon scattering Electron-electron scattering Electron-positron scattering Compton scattering Inelastic scattering Click on a diagram to jump to the code & download links… Continue Reading →
% chain.tex : % \begin{filecontents*}{chainofrings.asy} struct chainOfRings{ int n; // number of rings real w; pair origin; pen[] clrA={deepgreen,deepblue}; pen[] clrB={white,lightyellow,palered}; guide qring; real Rscaled(int); real rscaled(int); real eps; void drawHalf(int i,real Rt,real rt, pair p,real phi){ qring=rotate(phi)*(arc((0,0),Rt,-eps,90+eps)–reverse(arc((0,0),rt,-eps,90+eps))–cycle); radialshade(shift(p)*qring ,clrA[i%clrA.length],… Continue Reading →
\documentclass{article} \usepackage[inline]{asymptote} \usepackage{lmodern} \begin{document} \begin{asy} size(300,200,IgnoreAspect); import graph; real F(real t){return 4/sqrt(1+t^4);} real f(real x){return simpson(F,x,2x);} pen axPen=darkblue; pen fPen=red+1bp; draw(graph(f,-7,7,n=200),fPen); string noZero(real x) {return (x==0)?””:string(x);} defaultpen(fontsize(10pt)); xaxis(axPen,LeftTicks(noZero,Step=2)); yaxis(axPen,RightTicks(noZero,Step=0.5)); label(“$f:x\mapsto \displaystyle\int_x^{2x}” +”\frac{4}{\sqrt{1+t^4}}\, \textrm{d}t$” ,(1.7,f(1.7)),NE); \end{asy} \end{document} Source: TeX.SE Author: g.kov… Continue Reading →
(Reader, this is going to be a long, ranty, rambling piece; I apologise beforehand.) There are LaTeX packages for typesetting all kinds of things. And sometimes, there are more than one LaTeX packages that can do (almost) the same thing… Continue Reading →
Nach langer und gründlicher Vorbereitung wurde gestern Zotero 7 freigegeben, und die neue Version ist schön geworden. Nachdem ich zwei Jahre lang Zotero 6 unter macOS mit Rosetta betrieben habe, ist der Performance-Zuwachs durch die neue native Version auch unter Apple Silicon… Continue Reading →
\documentclass[border=10pt]{standalone} \usepackage{textgreek} \usepackage[inline]{asymptote} \usepackage{lmodern} \begin{document} \begin{asy} size(200); import graph; pair[] botP={(0,0.09),(0.252,0.196),(0.383,0.429),(0.479,0.588), (0.574,0.668),(0.733,0.726),(0.883,0.747),(1,0.747),}; pair[] topP={(0,0.341),(0.252,0.451),(0.383,0.677),(0.479,0.841), (0.574,0.92),(0.733,0.977),(0.883,0.993),(1,1),}; pair[] midP=0.5*(topP+botP); guide gtop=graph(topP,operator..); guide gbot=graph(botP,operator..); guide gmid=graph(midP,operator..); real f(real x){ real t=times(gmid,x)[0]; return point(gmid,t).y; }; real s(real x){ real tt=times(gtop,x)[0]; real tb=times(gbot,x)[0]; return point(gtop,tt).y-point(gbot,tb).y;… Continue Reading →
\documentclass[border=10pt]{standalone} \usepackage{asymptote} \begin{document} \begin{asy}[width=\the\linewidth,inline=true] settings.outformat=”pdf”; settings.render=0; settings.prc=false; import three; import solids; unitsize(1cm); currentprojection = orthographic(5,4,2); path3 x = (-1,0,0)–(4.5,0,0); draw(x,EndArrow3); label(“$x$”,(4.7,0,0)); path3 y = (0,-1,0)–(0,4.5,0); draw(y,EndArrow3); label(“$y$”,(0,4.7,0)); path3 z = (0,0,-1)–(0,0,4.5); draw(z,EndArrow3); label(“$z$”,(0,0,4.7)); label(“$O$”,(0,-0.3,-0.5)); path3 a = arc(O,3,0,0,90,0); draw(a); revolution… Continue Reading →
Es mag vorkommen, dass einem die eine oder die andere Anmerkung auf der Emacs-Devel-Liste entgeht. Aber dann gibt es ja immer noch die wöchentliche Zusammenfassung der Emacs News von Sacha Chua. In der heutigen Ausgabe verlinkt sie einen Teil-Thread, in… Continue Reading →
Nach einer längeren Diskussion hat Tassilo Horn heute Morgen bekanntgegeben, dass AUCTeX, die Entwicklungsumbegung für (La)TeX in Emacs, nicht mehr als Tarball verteilt werde. AUCTeX kann seitdem nur noch über das Archiv ELPA bezogen werden. AUCTeX 13.3 war demnach die letzte… Continue Reading →
The conventional 3D coordinate system at the CMS detector with definition of the azimuthal angle φ. It is officially described in this paper. For more coordinate systems, please see the “coordinates” tag. For the definition of pseudorapidity, please see here…. Continue Reading →
The “LaTeX Tagged PDF” project is now advanced enough that more and more people start using it. We have therefore begun with building usage documentation that is not scattered across different repositories as this is the case at the moment…. Continue Reading →
Writing abstracts and conference submissions is a key element of academic life, yet, I find that there is little guidance for those new to the activity. There are many things to know that will (in my experience) drastically increase your… Continue Reading →
\documentclass[border=10pt]{standalone} \usepackage{asymptote} \begin{document} \begin{asy}[inline=true] import graph3; real w=9cm, h=1.618w; size(w,h); currentprojection=orthographic(camera=(-13,-8.6,59),up=Z,target=(0.5,0.5,3),zoom=1); import fontsize; defaultpen(fontsize(9pt)); texpreamble(“\usepackage{siunitx}\usepackage{lmodern}”); pen linePen=darkblue+0.9bp; pen grayPen=gray(0.3)+0.8bp; pen dashPen=gray(0.3)+0.8bp+linetype(new real[] {5,5}); pen patchFillPen=paleblue; pen planeFillPen=deepgreen+opacity(0.3); triple[][] p={ // Bicubic Bezier patch control points {(1 ,0.3,0),(1 ,0.5,-1),(1 ,0.6,1),(1 ,1,0),},… Continue Reading →
\documentclass[border=10pt]{standalone} \usepackage[inline]{asymptote} \begin{document} \begin{asy} settings.render = 0; settings.prc = false; import graph3; real unit = 0.1cm; unitsize(unit); defaultpen(fontsize(10pt)); triple eyeDirection = dir((-2,-2,0.7)); currentprojection = orthographic(eyeDirection); triple translateDirection = dir(cross(Z, eyeDirection)); void drawBehind(path3 thepath, pen pen=currentpen, real backOpacity = 1.0, real… Continue Reading →
\documentclass[border=10pt]{standalone} \usepackage{asymptote} \begin{document} \begin{asy}[width=\the\linewidth,inline=true] unitsize(1cm); path a = (1,2.4)–(4,0.6)..(4.5,1)..(4.1,1.9)..(3.9,2)..cycle; draw(a); fill(a,cyan); path b = (0,3)–(5,0); draw(b,linewidth(2)); path c = shift(4,0.6)*scale(0.6)*unitcircle; draw(c,red+dashed); path d = (5,1.2)–(6,1.8); draw(d,EndArrow); path e = shift(8,3)*scale(2)*unitcircle; draw(e,red+dashed); path f = (9.4,1.6)–(6.1,3.58); draw(f,linewidth(2)); path g = (8,2.44)..(8.8,3.2)..(8.6,3.8)..(8.4,4.1);… Continue Reading →
Emacs 29.4 ist heute veröffentlicht worden. Und with a little help from my friends gelang es mir, auch die letzten Unzulänglichkeiten beim Kompilieren unter macOS Sonoma zu beseitigen. Entpacken muss man den Tarball nun auf der Kommandozeile. Aber erst wenn… Continue Reading →
The periodic table is a huge chart that organizes all known chemical elements by their atomic number and other properties. It makes it easy to see their relationships by grouping similar ones together. This table is essential for chemists and… Continue Reading →
I haven’t blogged for a while. I owe you an apology and an explanation, so here goes… Why I’m not blogging I’ve been reflecting a lot over the last few years on why I don’t really blog anymore. I think… Continue Reading →
We sent the 2024-06-01 release (patch level 1) of the LaTeX kernel to CTAN. By now it should be available to most users via TeX Live or MiKTeX. The LaTeX Tagged PDF project As with the previous release the team… Continue Reading →
Die letzte Version von BibTeX ist bekanntlich 0.99. Oren Patashniks Anleitung „BibTeXing“ trägt das Datum vom 8. Februar 1988, und diese Version ist noch immer Teil des BibTeX-Pakets, das mit den heutigen TeX-Distributionen ausgeliefert wird, hier beispielhaft TeX Live 2024: % bibtex… Continue Reading →
PGFplots.netの開始後、私はpgfplotsでさらに実験をしました。私がいつものように各グラフィックソフトウェアで行うように、フラクタルをどのように表現できるか、そしてそれによって有用または興味深い側面があるかどうかを考えました。ここでは速度やメモリスペースは二次的なもので、時間とともに容量は変わります。
リンデンマイヤーシステム、通称L-システムは、「置換システム」です：ある（グラフィック）オブジェクトの部分が、最も単純な場合にはその縮小されたオブジェクト自体に置き換えられます。これが繰り返され、例えば再帰的に行われます。これにより、非常に複雑なフラクタル構造が生まれ、同時に非常にシンプルに定義されることがあります。
ここでは、繰り返し関数システム、略してIFSについて扱います。ここでは繰り返し変換が行われます。空間が何度も自分自身にマッピングされます。このプロセスにはさまざまなマッピング規則があり得ます。理想的にはこれを無限に行い、すべての間で不変である空間内の集合を考察します。この集合はフラクタルになる可能性があります！ 理論はさておき、Wikipediaで基本的な内容を、そして素晴らしい本でより深く理解することができます。では、これをどのように生成するのでしょうか？ 最も簡単な方法は「カオスゲーム」と呼ばれるものです。一点を取り、その点に一つの変換を適用します。変換によって不変である点集合に関わるため、目的の点は集合内に落ちなければなりません。この新しい点でプロセスを繰り返し、何千回も繰り返して図が浮かび上がるまで続けます。
TUGboat volume 45, number 1, has been mailed to TUG members. It is also available online and from the TUG store. In addition, prior TUGboat issue 44:3 is now publicly available. The next issue will be the TUG’24 proceedings; the… Continue Reading →
\documentclass[border=10pt]{standalone} \usepackage{lmodern} \usepackage{upgreek} \usepackage[inline]{asymptote} \begin{document} \begin{asy}[width=\the\linewidth,inline=true] settings.outformat=”pdf”; settings.render=0; settings.prc=false; import three; import graph3; import grid3; currentprojection=obliqueX; //Draw Axes pen thickblack = black+0.75; real axislength = 1.0; draw(L=Label(“$x$”, position=Relative(1.1), align=SW), O–axislength*X,thickblack, Arrow3); draw(L=Label(“$y$”, position=Relative(1.1), align=E), O–axislength*Y,thickblack, Arrow3); draw(L=Label(“$z$”, position=Relative(1.1), align=N), O–axislength*Z,thickblack,… Continue Reading →
This post contains Minkowski diagrams of flat spacetime with light cones to illustrate the causal structure, as well as graphical interpretations of Lorentz transformations (“boosts”), and more. Some figures were inspired by Very special relativity – An illustrated guide by… Continue Reading →
Penrose diagram of Minkowski and Schwarzschild metrics to illustrate the causal structure of different spacetime geometries. Lightlike worldlines remain at 45 degrees as indicated by the photons and light cones, i.e. the diagrams are conformal. The grid indicates lines of… Continue Reading →
Kruskal diagram of Schwarzschild spacetime with light cones to illustrate the causal structure. Using Kruskal-Szekeres coordinates, lightlike worldlines remain at 45 degrees, i.e. the diagrams are conformal. The grid indicates lines of constant r and t. The horizon is at… Continue Reading →
The team have made development releases of the LaTeX kernel available for some time, to allow active users and developers to test new features. We have now extended this concept to cover the core of expl3 (packages l3kernel and l3backend)… Continue Reading →
Hasse diagrams illustrating how quadrilaterals are related, and marking congruent and right angles, as well as same length sides with a custom macro via pic. Inspired by this image on Wikimedia Commons. Most basic diagram to relate squares, rectangles, rhombi,… Continue Reading →
The call for papers for TUG’24 has been extended to June 1, as long as there is space in the schedule: cfp info (any TeX or typography-related topic is welcome). The bursary (financial assistance) deadline is also extended, to May… Continue Reading →
Some examples of neural network architectures: deep neural networks (DNNs), a deep convolutional neural network (CNN), an autoencoders (encoder+decoder), and the illustration of an activation function in neurons. Basic idea The full LaTeX code at the bottom of this post… Continue Reading →
While a word cloud is a pretty picture made of words, it’s a tool that can visualize the importance of topics or keywords, or how often a word appears in a text. Bigger words indicate higher frequency. Word clouds can… Continue Reading →
\documentclass[border=10pt]{standalone} \usepackage{asymptote} \begin{document} \begin{asy}[width=\the\linewidth,inline=true] settings.outformat=”pdf”; settings.render=0; settings.prc=false; size(300); import solids; currentprojection=orthographic ( camera=(8,5,4), up=(0,0,1), target=(2,2,2), zoom=0.5 ); // save predefined 2D orientation vectors pair NN=N; pair SS=S; pair EE=E; pair WW=W; //%points on cube triple A = (0,0,0); triple B… Continue Reading →
\documentclass[border=10pt]{standalone} \usepackage{lmodern} \usepackage{upgreek} \usepackage[inline]{asymptote} \begin{document} \begin{asy}[width=\the\linewidth,inline=true] import graph; import roundedpath; import math; //texpreamble(“\usepackage{upgreek}”); defaultpen(fontsize(10pt)); real sc=2; unitsize(sc*1bp); // 1. bounding ellipse guide ell=(150,60)..(75,120)..(3.4,60)..(75,0)..cycle; // 2. day pen penA=rgb(0.773,0.831,0.882); pen penB=rgb(0.09,0.09,0.09); pair a=(70,60); pair b=(100,60); fill(box((0,0),(90,120)),penA); axialshade(box((0,0),(100,120)),penA,a, extenda=false,penB,b, extendb=false); // night… Continue Reading →
Die zweite, verbesserte und erweiterte Ausgabe des LaTeX Cookbook ist diesen Monat, März 2024, in englischer Sprache erschienen. Die erste Ausgabe, veröffentlicht in 2015, wurde überarbeitet und die Code-Beispiele wurden aktualisiert, um mit den neuesten Klassen und Paketen von LaTeX… Continue Reading →