Mdthbs

Trivial cases of shared_ptr and weak_ptr failing

What advantages do focused Arrows of Slaying have over more generic ones?

Does the Intel 8085 CPU use real memory addresses?

Why alcohol had been selected as fuel for the first American space rockets?

Alphanumeric Line and Curve Counting

What are the arguments for California’s nonpartisan blanket (jungle) primaries?

Is this artwork (used in a video game) real?

Finding the package which provides a given command

Animal Shelter Management C++

How to determine the optimal threshold to achieve the highest accuracy

Cine footage fron Saturn V launch's

Why don't commercial aircraft adopt a slightly more seaplane-like design to allow safer ditching in case of emergency?

What is the word for "event executor"?

How fast does a character need to move to be effectively invisible?

Can a dragon's breath weapon pass through Leomund's Tiny Hut?

Bone Decomposition

Is it OK to use personal email ID for faculty job applications or should we use (current) institute's ID

What powers the air required for pneumatic brakes in aircraft?

What happens when I team swap while I have Pokemon inside a gym?

Cauchy reals and Dedekind reals satisfy "the same mathematical theorems"

What is the German word or phrase for "village returning to forest"?

Do I need a 50/60Hz notch filter for battery powered devices?

Is it rude to refer to janitors as 'floor people'?

How can I leave a car for someone if we can't meet in person?

Construct, in some manner, a four-dimensional “RegionPlot”

Labeling distinct objects produced by Show[RegionPlot3D's]How to create this four-dimensional cube animation?Four-way logarithmic plotRegionPlot not plotting some regionsList of Inequalities in RegionPlot with different colorsHow can I create a four dimensional plot (3D space + color) of the data provided?Creating a graphic with four rectangles and four pointsHow to visualize four-dimensional data?Plot four dimensional data consisting of discrete and continuous variables?RegionPlot misses a corner when plotting a two-dimensional regionHow to use ColorSlider for some objects?

.everyoneloves__top-leaderboard:empty,.everyoneloves__mid-leaderboard:empty,.everyoneloves__bot-mid-leaderboard:empty{ margin-bottom:0;
}

4

$begingroup$

Let me abuse some Mathematica notation and formulate the following "command":

Show[RegionPlot4D[(Q1 - Q4)^2 < 16 Q3^2 && 

   Q1^2 + 4 Q1 Q2 + 16 Q2 (Q2 + Q3) + 12 Q2 Q4 + Q4^2 < 

    4 Q2 + 2 Q1 Q4 && Q1 > 0 && Q2 > 0 && Q3 > 0 && Q4 > 0, {Q1, 0, 

   6/61}, {Q2, 0, 2/9}, {Q3, 0, 1/32}, {Q4, 0, 1/6}], 

 RegionPlot4D[

  Q4 > 0 && Q2 > 0 && Q3 > 0 && Q1 + 4 (Q2 + Q3) + 3 Q4 < 1 && 

   4 Q2 + 9 Q4 < Q1, {Q1, 0, 6/61}, {Q2, 0, 2/9}, {Q3, 0, 1/32}, {Q4, 

   0, 1/6}], 

 RegionPlot4D[

  Q4 > 0 && Q2 > 0 && Q3 > 0 && Q1 + 4 (Q2 + Q3) + 3 Q4 < 1 && 

   2 (Q2 + Q3) + 3 Q4 < Q1, {Q1, 0, 6/61}, {Q2, 0, 2/9}, {Q3, 0, 

   1/32}, {Q4, 0, 1/6}]]

(Of course, there is a RegionPlot3D command, but no RegionPlot4D one.)

Can this be processed/interpreted in some manner? (use of coloring,...)

Also, these three "RegionPlot"s could be considered individually (challenging enough).

These pertain to certain quantum-information-theoretic problems concerned with probabilities of (bound) entanglement.

The problem as put is very much a direct 4D analogue of the 3D problem

Labeling distinct objects produced by Show[RegionPlot3D's]

that kglr answered. So, perhaps I should just try fixing (in various ways) one of the four coordinates and approaching the problem in the very same manner as there. (In fact, the constraints are set up in the same order both times, with the first one each times being the "PPT" one. Incidentally, the "PPT" body should be convex, but not the other two.)

plotting graphics color dimension-reduction

share|improve this question

edited 8 hours ago

Paul B. Slater

asked 11 hours ago

Paul B. SlaterPaul B. Slater

76344 silver badges1414 bronze badges

$endgroup$

add a comment | 

4

$begingroup$

Let me abuse some Mathematica notation and formulate the following "command":

Show[RegionPlot4D[(Q1 - Q4)^2 < 16 Q3^2 && 

   Q1^2 + 4 Q1 Q2 + 16 Q2 (Q2 + Q3) + 12 Q2 Q4 + Q4^2 < 

    4 Q2 + 2 Q1 Q4 && Q1 > 0 && Q2 > 0 && Q3 > 0 && Q4 > 0, {Q1, 0, 

   6/61}, {Q2, 0, 2/9}, {Q3, 0, 1/32}, {Q4, 0, 1/6}], 

 RegionPlot4D[

  Q4 > 0 && Q2 > 0 && Q3 > 0 && Q1 + 4 (Q2 + Q3) + 3 Q4 < 1 && 

   4 Q2 + 9 Q4 < Q1, {Q1, 0, 6/61}, {Q2, 0, 2/9}, {Q3, 0, 1/32}, {Q4, 

   0, 1/6}], 

 RegionPlot4D[

  Q4 > 0 && Q2 > 0 && Q3 > 0 && Q1 + 4 (Q2 + Q3) + 3 Q4 < 1 && 

   2 (Q2 + Q3) + 3 Q4 < Q1, {Q1, 0, 6/61}, {Q2, 0, 2/9}, {Q3, 0, 

   1/32}, {Q4, 0, 1/6}]]

(Of course, there is a RegionPlot3D command, but no RegionPlot4D one.)

Can this be processed/interpreted in some manner? (use of coloring,...)

Also, these three "RegionPlot"s could be considered individually (challenging enough).

These pertain to certain quantum-information-theoretic problems concerned with probabilities of (bound) entanglement.

The problem as put is very much a direct 4D analogue of the 3D problem

Labeling distinct objects produced by Show[RegionPlot3D's]

that kglr answered. So, perhaps I should just try fixing (in various ways) one of the four coordinates and approaching the problem in the very same manner as there. (In fact, the constraints are set up in the same order both times, with the first one each times being the "PPT" one. Incidentally, the "PPT" body should be convex, but not the other two.)

plotting graphics color dimension-reduction

share|improve this question

edited 8 hours ago

Paul B. Slater

asked 11 hours ago

Paul B. SlaterPaul B. Slater

76344 silver badges1414 bronze badges

$endgroup$

add a comment | 

$begingroup$

Let me abuse some Mathematica notation and formulate the following "command":

Show[RegionPlot4D[(Q1 - Q4)^2 < 16 Q3^2 && 

   Q1^2 + 4 Q1 Q2 + 16 Q2 (Q2 + Q3) + 12 Q2 Q4 + Q4^2 < 

    4 Q2 + 2 Q1 Q4 && Q1 > 0 && Q2 > 0 && Q3 > 0 && Q4 > 0, {Q1, 0, 

   6/61}, {Q2, 0, 2/9}, {Q3, 0, 1/32}, {Q4, 0, 1/6}], 

 RegionPlot4D[

  Q4 > 0 && Q2 > 0 && Q3 > 0 && Q1 + 4 (Q2 + Q3) + 3 Q4 < 1 && 

   4 Q2 + 9 Q4 < Q1, {Q1, 0, 6/61}, {Q2, 0, 2/9}, {Q3, 0, 1/32}, {Q4, 

   0, 1/6}], 

 RegionPlot4D[

  Q4 > 0 && Q2 > 0 && Q3 > 0 && Q1 + 4 (Q2 + Q3) + 3 Q4 < 1 && 

   2 (Q2 + Q3) + 3 Q4 < Q1, {Q1, 0, 6/61}, {Q2, 0, 2/9}, {Q3, 0, 

   1/32}, {Q4, 0, 1/6}]]

(Of course, there is a RegionPlot3D command, but no RegionPlot4D one.)

Can this be processed/interpreted in some manner? (use of coloring,...)

Also, these three "RegionPlot"s could be considered individually (challenging enough).

These pertain to certain quantum-information-theoretic problems concerned with probabilities of (bound) entanglement.

The problem as put is very much a direct 4D analogue of the 3D problem

Labeling distinct objects produced by Show[RegionPlot3D's]

that kglr answered. So, perhaps I should just try fixing (in various ways) one of the four coordinates and approaching the problem in the very same manner as there. (In fact, the constraints are set up in the same order both times, with the first one each times being the "PPT" one. Incidentally, the "PPT" body should be convex, but not the other two.)

plotting graphics color dimension-reduction

share|improve this question

edited 8 hours ago

Paul B. Slater

asked 11 hours ago

Paul B. SlaterPaul B. Slater

76344 silver badges1414 bronze badges

$endgroup$

Show[RegionPlot4D[(Q1 - Q4)^2 < 16 Q3^2 && 

   Q1^2 + 4 Q1 Q2 + 16 Q2 (Q2 + Q3) + 12 Q2 Q4 + Q4^2 < 

    4 Q2 + 2 Q1 Q4 && Q1 > 0 && Q2 > 0 && Q3 > 0 && Q4 > 0, {Q1, 0, 

   6/61}, {Q2, 0, 2/9}, {Q3, 0, 1/32}, {Q4, 0, 1/6}], 

 RegionPlot4D[

  Q4 > 0 && Q2 > 0 && Q3 > 0 && Q1 + 4 (Q2 + Q3) + 3 Q4 < 1 && 

   4 Q2 + 9 Q4 < Q1, {Q1, 0, 6/61}, {Q2, 0, 2/9}, {Q3, 0, 1/32}, {Q4, 

   0, 1/6}], 

 RegionPlot4D[

  Q4 > 0 && Q2 > 0 && Q3 > 0 && Q1 + 4 (Q2 + Q3) + 3 Q4 < 1 && 

   2 (Q2 + Q3) + 3 Q4 < Q1, {Q1, 0, 6/61}, {Q2, 0, 2/9}, {Q3, 0, 

   1/32}, {Q4, 0, 1/6}]]

share|improve this question

edited 8 hours ago

Paul B. Slater

asked 11 hours ago

Paul B. SlaterPaul B. Slater

76344 silver badges1414 bronze badges

share|improve this question

edited 8 hours ago

Paul B. Slater

asked 11 hours ago

Paul B. SlaterPaul B. Slater

76344 silver badges1414 bronze badges

asked 11 hours ago

Paul B. SlaterPaul B. Slater

76344 silver badges1414 bronze badges

asked 11 hours ago

Paul B. SlaterPaul B. Slater

76344 silver badges1414 bronze badges

2 Answers
2

active

oldest

votes

4

$begingroup$

You can define a 4D region with

R = ImplicitRegion[(Q1 - Q4)^2 < 16 Q3^2 && 

      Q1^2 + 4 Q1 Q2 + 16 Q2 (Q2 + Q3) + 12 Q2 Q4 + Q4^2 < 

      4 Q2 + 2 Q1 Q4 && Q1 > 0 && Q2 > 0 && Q3 > 0 && Q4 > 0,

      {Q1, Q2, Q3, Q4}]

and then check for region membership of any point. For example, make a list of lots of points in 4D and pick out those that lie inside of R:

P = Select[Tuples[Range[0, 1/4, 1/128], 4], Element[#, R] &];

Length[P]

(*    84579    *)

These can be plotted in many ways, for example by projecting out the fourth dimension and using only the first, second, third dimension as coordinate axes:

ListPointPlot3D[P[[All, {1, 2, 3}]]]

For a convex set, you can construct the convex hull in 3D for such a projection, for better visibility than the point cloud:

ConvexHullMesh[P[[All, {1, 2, 3}]], Boxed -> True, Axes -> True]

share|improve this answer

answered 10 hours ago

RomanRoman

13.8k11 gold badge1919 silver badges5151 bronze badges

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Could one use ListPointPlot3D with multiple point sets, using different colors?
  $endgroup$
  – Paul B. Slater
  7 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @PaulB.Slater Yes you can.
  $endgroup$
  – Roman
  6 hours ago
  

  
  
  
  

add a comment | 

1

$begingroup$

Using Graphics3D with VertexColors based on the fourth column is much faster than using ListPointPlot3D.

With a smaller version of Roman's P (to stay within my cloud credit limits):

P = Select[Tuples[Range[0, 1/4, 1/64], 4], Element[#, R] &];



Graphics3D[{PointSize[Small], Point[P[[All, ;; 3]], 

    VertexColors -> (Hue /@ P[[All, 4]])]}] // RepeatedTiming

versus two alternative ways to use ListPointPlot3D:

ListPointPlot3D[Style[#[[;;3]], Hue @ #[[4]]]& /@ P,

   BaseStyle -> PointSize[Small]] // RepeatedTiming

ListPointPlot3D[List /@ P[[All, ;; 3]], 

  PlotStyle -> (Hue /@ P[[All, 4]]), 

  BaseStyle -> PointSize[Small]] // RepeatedTiming

share|improve this answer

answered 2 hours ago

kglrkglr

205k1010 gold badges233233 silver badges463463 bronze badges

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  So, can one jointly plot these results (presumably using different coloration schemes,...) with the parallel results based on one or both of the two other constraints given in the statement of the question? The expectation is that there should be some very small ("bound entanglement") overlap, if at all, between the points for the first constraint and those for either of the other two subsequent constraints. (Only the first constraint should yield a convex body, though.)
  $endgroup$
  – Paul B. Slater
  1 hour ago
  
  
  

  
  
  
  

add a comment | 

Your Answer

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
});


}
});

draft saved

draft discarded

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

Name

Email

Required, but never shown

StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmathematica.stackexchange.com%2fquestions%2f202195%2fconstruct-in-some-manner-a-four-dimensional-regionplot%23new-answer', 'question_page');
}
);

Post as a guest

Name

Email

Required, but never shown

4

$begingroup$

You can define a 4D region with

R = ImplicitRegion[(Q1 - Q4)^2 < 16 Q3^2 && 

      Q1^2 + 4 Q1 Q2 + 16 Q2 (Q2 + Q3) + 12 Q2 Q4 + Q4^2 < 

      4 Q2 + 2 Q1 Q4 && Q1 > 0 && Q2 > 0 && Q3 > 0 && Q4 > 0,

      {Q1, Q2, Q3, Q4}]

and then check for region membership of any point. For example, make a list of lots of points in 4D and pick out those that lie inside of R:

P = Select[Tuples[Range[0, 1/4, 1/128], 4], Element[#, R] &];

Length[P]

(*    84579    *)

These can be plotted in many ways, for example by projecting out the fourth dimension and using only the first, second, third dimension as coordinate axes:

ListPointPlot3D[P[[All, {1, 2, 3}]]]

For a convex set, you can construct the convex hull in 3D for such a projection, for better visibility than the point cloud:

ConvexHullMesh[P[[All, {1, 2, 3}]], Boxed -> True, Axes -> True]

share|improve this answer

answered 10 hours ago

RomanRoman

13.8k11 gold badge1919 silver badges5151 bronze badges

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Could one use ListPointPlot3D with multiple point sets, using different colors?
  $endgroup$
  – Paul B. Slater
  7 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @PaulB.Slater Yes you can.
  $endgroup$
  – Roman
  6 hours ago
  

  
  
  
  

add a comment | 

4

$begingroup$

You can define a 4D region with

R = ImplicitRegion[(Q1 - Q4)^2 < 16 Q3^2 && 

      Q1^2 + 4 Q1 Q2 + 16 Q2 (Q2 + Q3) + 12 Q2 Q4 + Q4^2 < 

      4 Q2 + 2 Q1 Q4 && Q1 > 0 && Q2 > 0 && Q3 > 0 && Q4 > 0,

      {Q1, Q2, Q3, Q4}]

and then check for region membership of any point. For example, make a list of lots of points in 4D and pick out those that lie inside of R:

P = Select[Tuples[Range[0, 1/4, 1/128], 4], Element[#, R] &];

Length[P]

(*    84579    *)

These can be plotted in many ways, for example by projecting out the fourth dimension and using only the first, second, third dimension as coordinate axes:

ListPointPlot3D[P[[All, {1, 2, 3}]]]

For a convex set, you can construct the convex hull in 3D for such a projection, for better visibility than the point cloud:

ConvexHullMesh[P[[All, {1, 2, 3}]], Boxed -> True, Axes -> True]

share|improve this answer

answered 10 hours ago

RomanRoman

13.8k11 gold badge1919 silver badges5151 bronze badges

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Could one use ListPointPlot3D with multiple point sets, using different colors?
  $endgroup$
  – Paul B. Slater
  7 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @PaulB.Slater Yes you can.
  $endgroup$
  – Roman
  6 hours ago
  

  
  
  
  

add a comment | 

$begingroup$

You can define a 4D region with

R = ImplicitRegion[(Q1 - Q4)^2 < 16 Q3^2 && 

      Q1^2 + 4 Q1 Q2 + 16 Q2 (Q2 + Q3) + 12 Q2 Q4 + Q4^2 < 

      4 Q2 + 2 Q1 Q4 && Q1 > 0 && Q2 > 0 && Q3 > 0 && Q4 > 0,

      {Q1, Q2, Q3, Q4}]

and then check for region membership of any point. For example, make a list of lots of points in 4D and pick out those that lie inside of R:

P = Select[Tuples[Range[0, 1/4, 1/128], 4], Element[#, R] &];

Length[P]

(*    84579    *)

These can be plotted in many ways, for example by projecting out the fourth dimension and using only the first, second, third dimension as coordinate axes:

ListPointPlot3D[P[[All, {1, 2, 3}]]]

For a convex set, you can construct the convex hull in 3D for such a projection, for better visibility than the point cloud:

ConvexHullMesh[P[[All, {1, 2, 3}]], Boxed -> True, Axes -> True]

share|improve this answer

answered 10 hours ago

RomanRoman

13.8k11 gold badge1919 silver badges5151 bronze badges

$endgroup$

R = ImplicitRegion[(Q1 - Q4)^2 < 16 Q3^2 && 

      Q1^2 + 4 Q1 Q2 + 16 Q2 (Q2 + Q3) + 12 Q2 Q4 + Q4^2 < 

      4 Q2 + 2 Q1 Q4 && Q1 > 0 && Q2 > 0 && Q3 > 0 && Q4 > 0,

      {Q1, Q2, Q3, Q4}]

P = Select[Tuples[Range[0, 1/4, 1/128], 4], Element[#, R] &];

Length[P]

(*    84579    *)

ListPointPlot3D[P[[All, {1, 2, 3}]]]

ConvexHullMesh[P[[All, {1, 2, 3}]], Boxed -> True, Axes -> True]

share|improve this answer

answered 10 hours ago

RomanRoman

13.8k11 gold badge1919 silver badges5151 bronze badges

answered 10 hours ago

RomanRoman

13.8k11 gold badge1919 silver badges5151 bronze badges

answered 10 hours ago

RomanRoman

13.8k11 gold badge1919 silver badges5151 bronze badges

1

$begingroup$

Using Graphics3D with VertexColors based on the fourth column is much faster than using ListPointPlot3D.

With a smaller version of Roman's P (to stay within my cloud credit limits):

P = Select[Tuples[Range[0, 1/4, 1/64], 4], Element[#, R] &];



Graphics3D[{PointSize[Small], Point[P[[All, ;; 3]], 

    VertexColors -> (Hue /@ P[[All, 4]])]}] // RepeatedTiming

versus two alternative ways to use ListPointPlot3D:

ListPointPlot3D[Style[#[[;;3]], Hue @ #[[4]]]& /@ P,

   BaseStyle -> PointSize[Small]] // RepeatedTiming

ListPointPlot3D[List /@ P[[All, ;; 3]], 

  PlotStyle -> (Hue /@ P[[All, 4]]), 

  BaseStyle -> PointSize[Small]] // RepeatedTiming

share|improve this answer

answered 2 hours ago

kglrkglr

205k1010 gold badges233233 silver badges463463 bronze badges

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  So, can one jointly plot these results (presumably using different coloration schemes,...) with the parallel results based on one or both of the two other constraints given in the statement of the question? The expectation is that there should be some very small ("bound entanglement") overlap, if at all, between the points for the first constraint and those for either of the other two subsequent constraints. (Only the first constraint should yield a convex body, though.)
  $endgroup$
  – Paul B. Slater
  1 hour ago
  
  
  

  
  
  
  

add a comment | 

1

$begingroup$

Using Graphics3D with VertexColors based on the fourth column is much faster than using ListPointPlot3D.

With a smaller version of Roman's P (to stay within my cloud credit limits):

P = Select[Tuples[Range[0, 1/4, 1/64], 4], Element[#, R] &];



Graphics3D[{PointSize[Small], Point[P[[All, ;; 3]], 

    VertexColors -> (Hue /@ P[[All, 4]])]}] // RepeatedTiming

versus two alternative ways to use ListPointPlot3D:

ListPointPlot3D[Style[#[[;;3]], Hue @ #[[4]]]& /@ P,

   BaseStyle -> PointSize[Small]] // RepeatedTiming

ListPointPlot3D[List /@ P[[All, ;; 3]], 

  PlotStyle -> (Hue /@ P[[All, 4]]), 

  BaseStyle -> PointSize[Small]] // RepeatedTiming

share|improve this answer

answered 2 hours ago

kglrkglr

205k1010 gold badges233233 silver badges463463 bronze badges

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  So, can one jointly plot these results (presumably using different coloration schemes,...) with the parallel results based on one or both of the two other constraints given in the statement of the question? The expectation is that there should be some very small ("bound entanglement") overlap, if at all, between the points for the first constraint and those for either of the other two subsequent constraints. (Only the first constraint should yield a convex body, though.)
  $endgroup$
  – Paul B. Slater
  1 hour ago
  
  
  

  
  
  
  

add a comment | 

$begingroup$

Using Graphics3D with VertexColors based on the fourth column is much faster than using ListPointPlot3D.

With a smaller version of Roman's P (to stay within my cloud credit limits):

P = Select[Tuples[Range[0, 1/4, 1/64], 4], Element[#, R] &];



Graphics3D[{PointSize[Small], Point[P[[All, ;; 3]], 

    VertexColors -> (Hue /@ P[[All, 4]])]}] // RepeatedTiming

versus two alternative ways to use ListPointPlot3D:

ListPointPlot3D[Style[#[[;;3]], Hue @ #[[4]]]& /@ P,

   BaseStyle -> PointSize[Small]] // RepeatedTiming

ListPointPlot3D[List /@ P[[All, ;; 3]], 

  PlotStyle -> (Hue /@ P[[All, 4]]), 

  BaseStyle -> PointSize[Small]] // RepeatedTiming

share|improve this answer

answered 2 hours ago

kglrkglr

205k1010 gold badges233233 silver badges463463 bronze badges

$endgroup$

P = Select[Tuples[Range[0, 1/4, 1/64], 4], Element[#, R] &];



Graphics3D[{PointSize[Small], Point[P[[All, ;; 3]], 

    VertexColors -> (Hue /@ P[[All, 4]])]}] // RepeatedTiming

ListPointPlot3D[Style[#[[;;3]], Hue @ #[[4]]]& /@ P,

   BaseStyle -> PointSize[Small]] // RepeatedTiming

ListPointPlot3D[List /@ P[[All, ;; 3]], 

  PlotStyle -> (Hue /@ P[[All, 4]]), 

  BaseStyle -> PointSize[Small]] // RepeatedTiming

share|improve this answer

answered 2 hours ago

kglrkglr

205k1010 gold badges233233 silver badges463463 bronze badges

answered 2 hours ago

kglrkglr

205k1010 gold badges233233 silver badges463463 bronze badges

answered 2 hours ago

kglrkglr

205k1010 gold badges233233 silver badges463463 bronze badges