Graphic representation of a triangle using ArrayPlotOverlapping ArrayPlotColor inversion using ArrayPlotPlotting Tupper's self-referential formula using ArrayPlotConstructing matrices from quantum states expressed in the bra-ket notationArrayPlot with logarithmic legendIntegral approximation using a matrix operatorNearest non-collinear/non-coplanar pointsHow to boost the performance of a function that approximates a 3D objectSpeeding up filling a matrix when approximating a double integralHow to achieve faster performance on plotting complex valued functions
Has a sovereign Communist government ever run, and conceded loss, on a fair election?
What should I do when a paper is published similar to my PhD thesis without citation?
How do I increase the number of TTY consoles?
Movie: boy escapes the real world and goes to a fantasy world with big furry trolls
Why restrict private health insurance?
Rationale to prefer local variables over instance variables?
The (Easy) Road to Code
Called into a meeting and told we are being made redundant (laid off) and "not to share outside". Can I tell my partner?
Is there a logarithm base for which the logarithm becomes an identity function?
How do you make a gun that shoots melee weapons and/or swords?
How exactly does an Ethernet collision happen in the cable, since nodes use different circuits for Tx and Rx?
Sampling from Gaussian mixture models, when are the sampled data independent?
If sound is a longitudinal wave, why can we hear it if our ears aren't aligned with the propagation direction?
What was so special about The Piano that Ada was willing to do anything to have it?
Under what conditions can the right to be silence be revoked in the USA?
(Codewars) Linked Lists-Sorted Insert
Too soon for a plot twist?
Idiom for feeling after taking risk and someone else being rewarded
Are these two graphs isomorphic? Why/Why not?
Short scifi story where reproductive organs are converted to produce "materials", pregnant protagonist is "found fit" to be a mother
Do black holes violate the conservation of mass?
Graphic representation of a triangle using ArrayPlot
When to use a QR code on a business card?
Computation logic of Partway in TikZ
Graphic representation of a triangle using ArrayPlot
Overlapping ArrayPlotColor inversion using ArrayPlotPlotting Tupper's self-referential formula using ArrayPlotConstructing matrices from quantum states expressed in the bra-ket notationArrayPlot with logarithmic legendIntegral approximation using a matrix operatorNearest non-collinear/non-coplanar pointsHow to boost the performance of a function that approximates a 3D objectSpeeding up filling a matrix when approximating a double integralHow to achieve faster performance on plotting complex valued functions
$begingroup$
So I need to write a function which takes natural integer $n$ and returns graphical representation of a matrix $n times n$ using ArrayPlot[].
This matrix has to be pixel approximation of equilateral triangle which get better and better as $n$ increases.
I figured out a set of equilateral triangle points which is $$P=(x,y) in mathbbR^2:y<sqrt3x+fracasqrt32,y<-sqrt3x+fracasqrt32,y>0$$
where $a$ is side length of this triangle.
f1[x_, a_] := -Sqrt[3]*x + (a*Sqrt[3])/2
f2[x_, a_] := Sqrt[3]*x + (a*Sqrt[3])/2
matrix[n_] := ConstantArray[0, n, n]
(...)
drawapprox[n_] := ArrayPlot[matrix[n], Mesh -> True]
So I make zero $n times n$ matrix and I want to put $1$ if a point belongs to $P$ but I don't know how to put together points from the plane to this 0-1 matrix to make it works. After that I just want to use ArrayPlot[] function to draw new 0-1 matrix which represents triangle.
How do I make up the missing (...) part?
plotting matrix approximation
asked 4 hours ago
apoxeiroapoxeiro
132
New contributor
apoxeiro is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
So I need to write a function which takes natural integer $n$ and returns graphical representation of a matrix $n times n$ using ArrayPlot[].
This matrix has to be pixel approximation of equilateral triangle which get better and better as $n$ increases.
I figured out a set of equilateral triangle points which is $$P=(x,y) in mathbbR^2:y<sqrt3x+fracasqrt32,y<-sqrt3x+fracasqrt32,y>0$$
where $a$ is side length of this triangle.
f1[x_, a_] := -Sqrt[3]*x + (a*Sqrt[3])/2
f2[x_, a_] := Sqrt[3]*x + (a*Sqrt[3])/2
matrix[n_] := ConstantArray[0, n, n]
(...)
drawapprox[n_] := ArrayPlot[matrix[n], Mesh -> True]
So I make zero $n times n$ matrix and I want to put $1$ if a point belongs to $P$ but I don't know how to put together points from the plane to this 0-1 matrix to make it works. After that I just want to use ArrayPlot[] function to draw new 0-1 matrix which represents triangle.
How do I make up the missing (...) part?
plotting matrix approximation
asked 4 hours ago
apoxeiroapoxeiro
132
New contributor
apoxeiro is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
So I need to write a function which takes natural integer $n$ and returns graphical representation of a matrix $n times n$ using ArrayPlot[].
This matrix has to be pixel approximation of equilateral triangle which get better and better as $n$ increases.
I figured out a set of equilateral triangle points which is $$P=(x,y) in mathbbR^2:y<sqrt3x+fracasqrt32,y<-sqrt3x+fracasqrt32,y>0$$
where $a$ is side length of this triangle.
f1[x_, a_] := -Sqrt[3]*x + (a*Sqrt[3])/2
f2[x_, a_] := Sqrt[3]*x + (a*Sqrt[3])/2
matrix[n_] := ConstantArray[0, n, n]
(...)
drawapprox[n_] := ArrayPlot[matrix[n], Mesh -> True]
So I make zero $n times n$ matrix and I want to put $1$ if a point belongs to $P$ but I don't know how to put together points from the plane to this 0-1 matrix to make it works. After that I just want to use ArrayPlot[] function to draw new 0-1 matrix which represents triangle.
How do I make up the missing (...) part?
plotting matrix approximation
asked 4 hours ago
apoxeiroapoxeiro
132
New contributor
apoxeiro is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
So I need to write a function which takes natural integer $n$ and returns graphical representation of a matrix $n times n$ using ArrayPlot[].
This matrix has to be pixel approximation of equilateral triangle which get better and better as $n$ increases.
I figured out a set of equilateral triangle points which is $$P=(x,y) in mathbbR^2:y<sqrt3x+fracasqrt32,y<-sqrt3x+fracasqrt32,y>0$$
where $a$ is side length of this triangle.
f1[x_, a_] := -Sqrt[3]*x + (a*Sqrt[3])/2
f2[x_, a_] := Sqrt[3]*x + (a*Sqrt[3])/2
matrix[n_] := ConstantArray[0, n, n]
(...)
drawapprox[n_] := ArrayPlot[matrix[n], Mesh -> True]
So I make zero $n times n$ matrix and I want to put $1$ if a point belongs to $P$ but I don't know how to put together points from the plane to this 0-1 matrix to make it works. After that I just want to use ArrayPlot[] function to draw new 0-1 matrix which represents triangle.
How do I make up the missing (...) part?
plotting matrix approximation
plotting matrix approximation
asked 4 hours ago
apoxeiroapoxeiro
132
New contributor
apoxeiro is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 4 hours ago
apoxeiroapoxeiro
132
New contributor
apoxeiro is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 4 hours ago
apoxeiroapoxeiro
132
New contributor
apoxeiro is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 4 hours ago
apoxeiroapoxeiro
132
asked 4 hours ago
apoxeiroapoxeiro
132
132
New contributor
apoxeiro is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
apoxeiro is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
apoxeiro is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Update: An alternative method using SparseArray:
ClearAll[sa, plot2]
sa[a_] := SparseArray[i_, j_ /;
a - i < f1[j - (a + Boole[OddQ[a]])/2, a] &&
a - i < f2[j - (a + Boole[OddQ[a]])/2, a] -> 1, a, a]
plot2[a_] := ArrayPlot[sa[a], Mesh -> All]
Row[plot2 /@ Range[3, 21, 2]]
Original answer:
aplot[a_] := ArrayPlot[Boole @ MapIndexed[
a - #2[[1]] < f1[#2[[2]] - (a + Boole[OddQ[a]])/2, a] &&
a - #2[[1]] < f2[#2[[2]] - (a + Boole[OddQ[a]])/2, a] &,
matrix[a], 2], Mesh -> All];
Row[Show[plot@#, Graphics[FaceForm[], EdgeForm[Thick, Red], SSSTriangle[#, #, #]]] & /@
Range[3, 21, 2]]
With a = 101; and Mesh -> None, we get
a = 1001;
ap1001 = ArrayPlot[Boole@MapIndexed[
a - #2[[1]] < f1[#2[[2]] - (a + Boole[OddQ[a]])/2, a] &&
a - #2[[1]] < f2[#2[[2]] - (a + Boole[OddQ[a]])/2, a] &,
matrix[a], 2], Mesh -> None];
Graphics[ap1001[[1]], FaceForm[], EdgeForm[Thick, Red],
SSSTriangle[1001, 1001, 1001]]
answered 2 hours ago
kglrkglr
188k10203421
$endgroup$
add a comment |
Your Answer
StackExchange.ifUsing("editor", function ()
return StackExchange.using("mathjaxEditing", function ()
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix)
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
);
);
, "mathjax-editing");
StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "387"
;
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function()
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled)
StackExchange.using("snippets", function()
createEditor();
);
else
createEditor();
);
function createEditor()
StackExchange.prepareEditor(
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: false,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: null,
bindNavPrevention: true,
postfix: "",
imageUploader:
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
,
onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);
);
apoxeiro is a new contributor. Be nice, and check out our Code of Conduct.
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmathematica.stackexchange.com%2fquestions%2f192959%2fgraphic-representation-of-a-triangle-using-arrayplot%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Update: An alternative method using SparseArray:
ClearAll[sa, plot2]
sa[a_] := SparseArray[i_, j_ /;
a - i < f1[j - (a + Boole[OddQ[a]])/2, a] &&
a - i < f2[j - (a + Boole[OddQ[a]])/2, a] -> 1, a, a]
plot2[a_] := ArrayPlot[sa[a], Mesh -> All]
Row[plot2 /@ Range[3, 21, 2]]
Original answer:
aplot[a_] := ArrayPlot[Boole @ MapIndexed[
a - #2[[1]] < f1[#2[[2]] - (a + Boole[OddQ[a]])/2, a] &&
a - #2[[1]] < f2[#2[[2]] - (a + Boole[OddQ[a]])/2, a] &,
matrix[a], 2], Mesh -> All];
Row[Show[plot@#, Graphics[FaceForm[], EdgeForm[Thick, Red], SSSTriangle[#, #, #]]] & /@
Range[3, 21, 2]]
With a = 101; and Mesh -> None, we get
a = 1001;
ap1001 = ArrayPlot[Boole@MapIndexed[
a - #2[[1]] < f1[#2[[2]] - (a + Boole[OddQ[a]])/2, a] &&
a - #2[[1]] < f2[#2[[2]] - (a + Boole[OddQ[a]])/2, a] &,
matrix[a], 2], Mesh -> None];
Graphics[ap1001[[1]], FaceForm[], EdgeForm[Thick, Red],
SSSTriangle[1001, 1001, 1001]]
answered 2 hours ago
kglrkglr
188k10203421
$endgroup$
add a comment |
$begingroup$
Update: An alternative method using SparseArray:
ClearAll[sa, plot2]
sa[a_] := SparseArray[i_, j_ /;
a - i < f1[j - (a + Boole[OddQ[a]])/2, a] &&
a - i < f2[j - (a + Boole[OddQ[a]])/2, a] -> 1, a, a]
plot2[a_] := ArrayPlot[sa[a], Mesh -> All]
Row[plot2 /@ Range[3, 21, 2]]
Original answer:
aplot[a_] := ArrayPlot[Boole @ MapIndexed[
a - #2[[1]] < f1[#2[[2]] - (a + Boole[OddQ[a]])/2, a] &&
a - #2[[1]] < f2[#2[[2]] - (a + Boole[OddQ[a]])/2, a] &,
matrix[a], 2], Mesh -> All];
Row[Show[plot@#, Graphics[FaceForm[], EdgeForm[Thick, Red], SSSTriangle[#, #, #]]] & /@
Range[3, 21, 2]]
With a = 101; and Mesh -> None, we get
a = 1001;
ap1001 = ArrayPlot[Boole@MapIndexed[
a - #2[[1]] < f1[#2[[2]] - (a + Boole[OddQ[a]])/2, a] &&
a - #2[[1]] < f2[#2[[2]] - (a + Boole[OddQ[a]])/2, a] &,
matrix[a], 2], Mesh -> None];
Graphics[ap1001[[1]], FaceForm[], EdgeForm[Thick, Red],
SSSTriangle[1001, 1001, 1001]]
answered 2 hours ago
kglrkglr
188k10203421
$endgroup$
add a comment |
$begingroup$
Update: An alternative method using SparseArray:
ClearAll[sa, plot2]
sa[a_] := SparseArray[i_, j_ /;
a - i < f1[j - (a + Boole[OddQ[a]])/2, a] &&
a - i < f2[j - (a + Boole[OddQ[a]])/2, a] -> 1, a, a]
plot2[a_] := ArrayPlot[sa[a], Mesh -> All]
Row[plot2 /@ Range[3, 21, 2]]
Original answer:
aplot[a_] := ArrayPlot[Boole @ MapIndexed[
a - #2[[1]] < f1[#2[[2]] - (a + Boole[OddQ[a]])/2, a] &&
a - #2[[1]] < f2[#2[[2]] - (a + Boole[OddQ[a]])/2, a] &,
matrix[a], 2], Mesh -> All];
Row[Show[plot@#, Graphics[FaceForm[], EdgeForm[Thick, Red], SSSTriangle[#, #, #]]] & /@
Range[3, 21, 2]]
With a = 101; and Mesh -> None, we get
a = 1001;
ap1001 = ArrayPlot[Boole@MapIndexed[
a - #2[[1]] < f1[#2[[2]] - (a + Boole[OddQ[a]])/2, a] &&
a - #2[[1]] < f2[#2[[2]] - (a + Boole[OddQ[a]])/2, a] &,
matrix[a], 2], Mesh -> None];
Graphics[ap1001[[1]], FaceForm[], EdgeForm[Thick, Red],
SSSTriangle[1001, 1001, 1001]]
answered 2 hours ago
kglrkglr
188k10203421
$endgroup$
Update: An alternative method using SparseArray:
ClearAll[sa, plot2]
sa[a_] := SparseArray[i_, j_ /;
a - i < f1[j - (a + Boole[OddQ[a]])/2, a] &&
a - i < f2[j - (a + Boole[OddQ[a]])/2, a] -> 1, a, a]
plot2[a_] := ArrayPlot[sa[a], Mesh -> All]
Row[plot2 /@ Range[3, 21, 2]]
Original answer:
aplot[a_] := ArrayPlot[Boole @ MapIndexed[
a - #2[[1]] < f1[#2[[2]] - (a + Boole[OddQ[a]])/2, a] &&
a - #2[[1]] < f2[#2[[2]] - (a + Boole[OddQ[a]])/2, a] &,
matrix[a], 2], Mesh -> All];
Row[Show[plot@#, Graphics[FaceForm[], EdgeForm[Thick, Red], SSSTriangle[#, #, #]]] & /@
Range[3, 21, 2]]
With a = 101; and Mesh -> None, we get
a = 1001;
ap1001 = ArrayPlot[Boole@MapIndexed[
a - #2[[1]] < f1[#2[[2]] - (a + Boole[OddQ[a]])/2, a] &&
a - #2[[1]] < f2[#2[[2]] - (a + Boole[OddQ[a]])/2, a] &,
matrix[a], 2], Mesh -> None];
Graphics[ap1001[[1]], FaceForm[], EdgeForm[Thick, Red],
SSSTriangle[1001, 1001, 1001]]
answered 2 hours ago
kglrkglr
188k10203421
edited 2 hours ago
answered 2 hours ago
kglrkglr
188k10203421
answered 2 hours ago
kglrkglr
188k10203421
answered 2 hours ago
kglrkglr
188k10203421
188k10203421
add a comment |
add a comment |
apoxeiro is a new contributor. Be nice, and check out our Code of Conduct.
apoxeiro is a new contributor. Be nice, and check out our Code of Conduct.
apoxeiro is a new contributor. Be nice, and check out our Code of Conduct.
apoxeiro is a new contributor. Be nice, and check out our Code of Conduct.
Thanks for contributing an answer to Mathematica Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmathematica.stackexchange.com%2fquestions%2f192959%2fgraphic-representation-of-a-triangle-using-arrayplot%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
