plot – Can Mathematica create zoomable plots with embedded text of different sizes?

I'm trying to figure out how to do something on MMa that is easy enough for Matlab. I some data points that each map a numeric parameter to a point in 2D space. I have to draw the values ​​of the parameters up to the 2D point. The code below is already done, even a little clumsily. "Data" is simulated with random numbers.

data = RandomReal[1, {200, 2}];
b = Table[{Text[i, data[[i]]]}, {i, 1, Length[data]}];
ListPlot[{0, 0}, PlotStyle -> PointSize[.004], PlotRange -> {{0, 1}, {0, 1}}, Epilog -> b]

So first of all, is there a way to draw JUST when I put in this "epilogue" b, without having to simulate this data point {0,0}. I can only ask ListPlot to put a test on a plot as an epilogue, and it will only drag the epilogs after certain data.

Secondly, is there a way to create a plot I can zoom in on, as text fonts are resized to remain readable? If you run the code above, the plot is cluttered to read, but if I could zoom and resize, it would be readable wherever I looked.

Cloud Deploy Dynamic Click Plot Plot

I was wondering if anyone had a solution explaining why the following code, which works in Mathematica 12.0, does not work with Cloud Deploy?

CloudDeploy@
 DynamicModule({pt = {(Pi)/2, 3}}, 
  ClickPane(
   Plot(3 Sin(x), {x, -6, 6}, 
    Epilog -> {Dynamic@Arrow({{1, 5}, pt}), Text("Extremum", {2, 5})},
     PlotRange -> 
     6), (With({x = (2 Round(-1/2 + #((1))/(Pi)) + 1) (Pi)/2}, 
      pt = {x, 3 Sin(x)})) &))

Thanks in advance

tracing – density plot out of bounds

I'm trying to draw a function Lkall (shown in the picture below) with two entries temp and n1d, but the function varies on several orders. And my density chart shows a white region (bottom left) where the value is quite high? Is there a log-log density chart? Or how should I create legends such that I can see the results for a wide range of Lkall?

enter the description of the image here

plot – ColorFunction based on the table index in ListLinePlot

ColorFunction specifies that for ListLinePlot he takes the $ x, y $ input data. However, I would like to take the array index (or usually an external array of the same length) as input for ColorFunction so, if we use a rainbow color palette, the oldest dots appear in purple and the last dots in red. An application would be a visualization of the long-term behavior of a system.

For example if we take

ListLinePlot(Table(E^-0.001 x {Cos(x), Sin(x)}, {x, 0, 100, 0.1}))

then the outer lines should be purple and gradually become red as the plot winds up.

Tick ​​length in the plot

I know I can manually adjust the tick length of the frame using FrameTickStyle. However, is there a way to globally increase the length of ticks?

plot – BoundaryDiscretizeRegion Plots does not work with ParametricPlot3D

I'm trying to mind this data

b = 0.042; a = 0.1075;
rh1 = 0.071553571428571;
rh2 = 0.077946428571429;
(Theta)1 = -(0.085497114090722/2);
(Theta)2 = (0.085497114090722)/2;
(Gamma)0 = 27.5925876895488499940256588160991668701171875`50.; 
(Gamma)1 = 27.6561421691630044961129897274076938629150390625`50.;
(Gamma)2 = 29.526641831934380633128967019729316234588623046875`50.;
(Gamma)3 = 35.430661411534771332298987545073032379150390625`50.;
(Gamma)4 = 44.104585229662689016549848020076751708984375`50.;
(Gamma)5 = 53.77374161874728741850049118511378765106201171875`50.;
B0 = -0.258727433320186828158426806112402118742465972900390625`50.;
C0 = -0.087231063588538659825388776880572549998760223388671875`50.;
D0 = -1.54343899231474868116720244870521128177642822265625`50.;
B1 = 10.8721158771190697933661795104853808879852294921875`50.;
C1 = 1.0083854268623009264871370760374702513217926025390625`50.;
D1 = 12.755787693798620097140883444808423519134521484375`50.;
B2 = 0.6119179333464430659006438872893340885639190673828125`50.;
C2 = 0.11419103062758979849622420488231000490486621856689453125`50.;
D2 = 0.56721637438979011225370641113840974867343902587890625`50.;
B3 = 0.1702199985379937718921183886777726002037525177001953125`50.;
C3 = 0.07329541454198429395461289459490217268466949462890625`50.;
D3 = 0.1560232223658888361939034439274109899997711181640625`50.;
B4 = 0.0526358651260851184705558125642710365355014801025390625`50.;
C4 = 0.04176822369822615066414783768777851946651935577392578125`50.;
D4 = 0.051253182800385883866045588774795760400593280792236328125`50.;
B5 = 0.01679753231958447390326227832701988518238067626953125`50.;
C5 = 0.022207085726827675842276477169434656389057636260986328125`50.;
D5 = 0.017742295388893665475382732665821094997227191925048828125`50.;
H1 = {{BesselJ(0, (Gamma)0*r) + B0*BesselY(0, (Gamma)0*r) + 
     C0*BesselI(0, (Gamma)0*r) + 
     D0*BesselK(0, (Gamma)0*r)}, {BesselJ(1, (Gamma)1*r) + 
      B1*BesselY(1, (Gamma)1*r) + C1*BesselI(1, (Gamma)1*r) + 
      D1*BesselK(1, (Gamma)1*r)}*(Cos((Theta))), {BesselJ(
       2, (Gamma)2*r) + B2*BesselY(2, (Gamma)2*r) + 
      C2*BesselI(2, (Gamma)2*r) + D2*BesselK(2, (Gamma)2*r)}*(Cos(
      2*(Theta))), {BesselJ(3, (Gamma)3*r) + 
      B3*BesselY(3, (Gamma)3*r) + C3*BesselI(3, (Gamma)3*r) + 
      D3*BesselK(3, (Gamma)3*r)}*(Cos(
      3*(Theta))), {BesselJ(4, (Gamma)4*r) + 
      B4*BesselY(4, (Gamma)4*r) + C4*BesselI(4, (Gamma)4*r) + 
      D4*BesselK(4, (Gamma)4*r)}*(Cos(
      4*(Theta))), {BesselJ(5, (Gamma)5*r) + 
      B5*BesselY(5, (Gamma)5*r) + C5*BesselI(5, (Gamma)5*r) + 
      D5*BesselK(5, (Gamma)5*r)}*(Cos(5*(Theta)))};
H2 = {{BesselJ(1, (Gamma)1*r) + B1*BesselY(1, (Gamma)1*r) + 
      C1*BesselI(1, (Gamma)1*r) + 
      D1*BesselK(1, (Gamma)1*r)}*(Sin((Theta))), {BesselJ(
       2, (Gamma)2*r) + B2*BesselY(2, (Gamma)2*r) + 
      C2*BesselI(2, (Gamma)2*r) + D2*BesselK(2, (Gamma)2*r)}*(Sin(
      2*(Theta))), {BesselJ(3, (Gamma)3*r) + 
      B3*BesselY(3, (Gamma)3*r) + C3*BesselI(3, (Gamma)3*r) + 
      D3*BesselK(3, (Gamma)3*r)}*(Sin(
      3*(Theta))), {BesselJ(4, (Gamma)4*r) + 
      B4*BesselY(4, (Gamma)4*r) + C4*BesselI(4, (Gamma)4*r) + 
      D4*BesselK(4, (Gamma)4*r)}*(Sin(
      4*(Theta))), {BesselJ(5, (Gamma)5*r) + 
      B5*BesselY(5, (Gamma)5*r) + C5*BesselI(5, (Gamma)5*r) + 
      D5*BesselK(5, (Gamma)5*r)}*(Sin(5*(Theta)))};
H = Join(H1, H2);
Eigvectors = 
{{-0.00032910702592332067748330550715383735242784158137713845786365866
618131449249`50., 
    0.0000619394300120392780844012821989786217898198231051515592104294
1747885144002`50., 
    0.0005547827300665782271433910475035989813436308122253333513903714
1848307835336`50., 
    0.0005231988120040556552360013802091916709121452211867352600736746
8527124122845`50., 
    0.0001838703756141756214053904725815494830601516198880360538176908
4779577600227`50., 1.`50., 
    2.535318998719537730027615020797307965593938101494039361034438`50.
*^-17, -2.
1199319771545881344744738949843672854921570996787640418875656`50.*^-
16, 1.34543416580296032974037527983559183583191075512792285969355953`
50.*^-15, 
    1.45414196658736704189109420869275005922675219240791977060328612`
50.*^-15, 
-2.917097488216128637398507230661172533566547614650862244192105116`50.
*^-14}, {4.
1393906816958560506978253749717613270207895244841348699741100140013322
45713633`50.*^-18, 
-9.14021353961675242207947861212444698545448700280830102418224`50.*^-
18, -2.909029886480655906567397243598961616405208425684555840862853`
50.*^-16, 
    9.3614156404083407742753906079531560632438588700394338002564902`
50.*^-16, 
    1.4128637809158172162529083345653765060314564044217952827602257`
50.*^-15, 
    2.90765574314389495791231923027726231261113923608199467872172016`
50.*^-14, 
-0.0000102487513305948084431870771189154082388487279146178514491923798
1836808159`50., 
-0.0002240825961280424559068758588142077514355999816542655770043371938
7236316922`50., 
-0.0005143836872790891355266039041046145928385094397241827389040327182
2346420488`50., 
-0.0012074595447196376182807727974712165509603740267021568252014645476
4359518489`50., 
    1.`50.}, 
{0.0004608033513713831258375485171807049504541716271843716959516879997
7954873463`50., 
-0.0000856174018654443306072450212002276545270315224574867444593157249
0976293488`50., 
-0.0007497256113880201907096291212615010208187874984455863008128208092
33944644`50., 
-0.0007045369820657110223994646630313088602108232772246448816068537928
9026644997`50., -1.`50., 
-0.0007292709021946642586591303431807983205254318563468210388878191979
3230329422`50., 
    1.612465340701469773140111230767500956284428913412180015912364`50.
*^-17, 2.2718176145494184590612295330354512566068520834977601089972492
`50.*^-16, 
    1.53374998822348400734702009686123657274307302110011805725316381`
50.*^-15, 
-6.6476932216263309515467886755298524111379493050733579115455005892`
50.*^-13, 
-3.4210817258822349903667884338340901589397780953005271635150603`50.*^
-16}, {3.9215110591163238921985484848432872986726068018374286243968374
`50.*^-16, 
-7.060293531811999168219332314229657629906880338977727849738489`50.*^-
17, -4.2203271327201239511388284905277631283833695511007867566252656`
50.*^-16, 
-1.10492079661353270253589364762728014029228771216039031875811473`50.*^
-15, -6.64447150372026487128378926830272110962921937953808918595995809
56`50.*^-13, 
-1.1039589080359062320096115641314423281295291969769716184211785`50.*^
-15, -0.00002193153145134803755895737369104039031458486962738630602584
085765083799767`50., 
-0.0004952446540505775859824195160651590958951137819892825972857427871
1851131332`50., 
-0.0013867066231735361951413009403097147160753784730872362437262964511
962098162`50., 1.`50., 
    0.0015242107960386576553082305181457021160941979625148388414183400
1581319880917`50.}, 
{-0.000721695041384639970379347844909717422462164250717250107153752199
92263667019`50., 
    0.0001341141851614028158479228936924702597153616176660938614165098
2407034412274`50., 
    0.0013214363877639745778778738053876766822419495682974748092042064
8012566633748`50., 1.`50., 
    0.0002029831726643346866436351146244634360890031726167254591278677
6861797776094`50., 
    0.0002977781820516691385431807618954168637544970611384250279080029
5039049646433`50., 
    1.4344546788155352577996314770057287699130055037444734390653782420
93035081086896`50.*^-18, 
-5.0168005290211820231440331061843788947295286084580853880737910939370
33563677789`50.*^-18, 
    1.297712171501468983410624722875930248222442436629399653403748406`
50.*^-14, 
    4.8581438122295662451507703426348866793651927344204790733055165`
50.*^-16, 
-4.0552917052426496603290162438647799902278269979897741182127621`50.*^
-16}, {-8.
235323830670512169881118021458569738049510303663170791226304`50.*^-17,
     9.23655360963475521664004862478283204162384908333810889082003`50.
*^-18, -7.
872020760977684814881212429986455457253066516284795301803299`50.*^-17,
 -1.296154100788077082551258188600238507468231933102631878490866991`
50.*^-14, 
    2.4385168962471148278190479611897767936639927505803644059180493`
50.*^-16, 
-2.0450432993050091825511873734756232069796967020622757330467207`50.*^
-16, -0.00006122399474276091388487955110005694087188105331930580248885
845825566637149`50., 
-0.0015861652476044066717707566467004430446023792304980359386936773699
7786889289`50., 1.`50., 
    0.0018686818872298847181351525985422925101326444010139838017798752
0983537635227`50., 
    0.0008791955018964318404070731849445697041615663396599332953553779
5866495493148`50.}, 
{-0.001580744502339414896539179840369942320380239654112722162971839684
154962524`50., 
    0.0003289875243886837776528933204461343854758217073002874974616918
7514762146841`50., 
    1.`50., -0.
0009728175599309765319619183142830433297403137404732184238142773216224
4252881`50., 
-0.0002522599989090151053284432215487695457841690756867243606866855825
535958794`50., 
-0.0000785975687305026448545819167358022930218343550901059664321527559
3472854784`50., 
-2.9859160441888262092813465351342666016122408696689304854323547603282
08137509329`50.*^-18, 
-5.116058689661065049487818532294625230857992745437944041028724491`50.
*^-14, -1.
1755737298383730580520312731546830494148662411819392897719667`50.*^-
16, -1.2655011041710821870181758690178517933359278620149434248094979`
50.*^-16, 
    6.640564452018317633907939020558928290820710031845098527571613`50.
*^-17}, {-1.
1057830913544361669733951539486951152289493830247499150239963`50.*^-
16, -2.363081701143659722879942836864166518743190830905134202347195`
50.*^-17, 
-5.108359693912843973911294522726808232669380070122321435568296463`50.
*^-14, 2.434711327966822362738131425038585790958945426419939438167281`
50.*^-17, 
    6.549004864251973982474258354586105422930739954128607600271419`50.
*^-17, -1.
1366687348301205975623936541232952034656131011204965921899129`50.*^-
16, 0.0003198544659064150541532486941729514891847165226407919351488775
9515285897949`50., -1.`50., 
-0.0029515001275693582121083534832353832974200229953610048870468754845
2592675859`50., 
-0.0012494216883185347043268372138726866888759617328994661540689855925
6588513197`50., 
-0.0007163867701357530554207893962970338177896660067841435430743099698
060169262`50.}, 
{-0.001687689286197699785669067051406701055823325566989708591650799350
28546454916`50., -1.`50., 
    0.0261069627679070011954391841099060896056894575306742869798623776
4444362989925`50., 
    0.0128124775781892929209661336591617074048585937965968486882684081
890850667266`50., 
    0.0072183327550258495931317314872393677087586332960887847130624619
1648616608986`50., 
    0.0045179985220927684774607925446066132752416709361615753462512216
825761743851`50., 
-5.962728273654544734495044158633264287143624080341275776310369434`50.
*^-14, -1.
22894867235371551095475331666109739751325961807560023423961793`50.*^-
15, 1.004785594164117355971128123493380117697773246297865098442237`50.
*^-17, -1.
13919807651009683115123456760653707110054408494576589209130413`50.*^-
15, -1.2079747110409626402292720978386539116276001400584523234139492`
50.*^-16}, 
{1.808526475002847594801973463269620688084868519645429305669613339`50.
*^-14, -5.
969185435205016837823427245246054469633834080993506438006781939`50.*^-
14, 3.08805526287246500425428402264016519031368661706228586545755311`
50.*^-15, 
    2.0586426135603362137833902198326297647002956589535961785063012`
50.*^-16, 
    7.9307944168456240437402614205078006959588119302476261811764927`
50.*^-16, 
-3.6782662894364863892475509209929013190151919350085249236678966`50.*^
-16, 1.`50., 
    0.0374050766055095015288445953609994506168469420062098350710965886
1876610146802`50., 
    0.0134600109022510329650372430591675355512145691096044172006040052
9863454521428`50., 
    0.0065283257970991131672355961829056296484904283757364644938075274
1590137059805`50., 
    0.0038649320987731052336756224552645495376819790980291023724402847
9247623006113`50.}, {1.`50., 
-0.0001484441797251027373835513255741263776559023318831909023630893804
590932471`50., 
    0.0024592397194208468772068156707164262284976757372885669910269049
2606679975748`50., 
    0.0015005312438479287455417456039735845815224520313779003073659163
1202244087766`50., 
    0.0009088942139718065447307708431438307251551632444673489694336995
7998167921769`50., 
    0.0005905464817700233861262550023893767570233648988605261846297219
8980340796028`50., 
-3.690391194295661686797560288286279485225137860116469033333616`50.*^-
16, -4.0386376430758020245668911832126660425875450686723454203692188`
50.*^-16, 
    1.2172850312878280837979078959830368288265953286580952089571358`
50.*^-16, 
-8.608407088469488809355424962462519273138095681824263875753515`50.*^-
17, -2.281642952879382399672649393634184780094337182121603198326391`
50.*^-17}};
Dcomplete = Annulus({0, 0}, {b, a});
Dhole = 
  Annulus({0, 0}, {rh1, rh2}, {(Theta)1, (Theta)2});
D = 
  RegionDifference(Dcomplete, Dhole);
BoundaryDiscretizeRegion(D, PrecisionGoal -> 5)

who produces this discretized region

enter the description of the image here

I want to produce a ParametricPlot3D like that

enter the description of the image here

but with the hole created in the area. I've already tried it with that

ParametricPlot3D({r Sin((Theta)), r Cos((Theta)), 
  Eigvectors((All, 1)).H((All, 1))}, {(Theta), 
   r} (Element) D, 
 Mesh -> {Range(0, 2 Pi, 2 Pi/50), 20}, Boxed -> False, Axes -> False,
  BoxRatios -> 1, BoundaryStyle -> Black)

who produces this

enter the description of the image here

it is clear that there is no resolution, that something is wrong; even by increasing the values ​​of PrecisionGoal and including AccuracyGoal In the region.

Tracing – Extending a 2D to 3D Plot

So having trouble making a graph of this potential in 3D

$ U (x) = frac {k ^ 2} {4g} – frac {k} {2} x ^ 2 + frac {k} {2} x ^ 4 $

That's what I have for 2D

setting k = 1 and g = 1

U(x_) := .25 - .5 x^2 + .25 x^4

Plot(U(x), {x, -1.5, 1.5})

enter the description of the image here

How can I extend this to 3D with mathematica?

plot – Addition of an identification letter to plots in a standard position

In many publications, it is customary to mark the diagrams of a large letter of identification – an example is shown below. What functionality of Mathematica is useful for adding such identifiers and how can it be used so that the relative position of this identifier is the same for all diagrams of similar dimensions, but not necessarily similar axis ranges?

enter the description of the image here

Plot: Change the number format on the axis of the graph

  1. I have to change the format to represent the numbers in abscissa. I want to keep the numbers 0,2,4,6,8,10 and put the degree, for example, on the tab "time, * 10 ^ 9 seconds" or keep numbers without diploma using the. abbreviation "time, nanoseconds".

  2. Is it possible to put y1 (t) in the frame? Place it in the upper right corner for example.

See the code below:

Plot(10^12*Sin(t/10^9), {t, 0, 10^10}, 
Axes -> None, Frame -> True, 
PlotStyle -> RGBColor(0., 0., 0.), 
FrameStyle -> Thick, 
PlotLabel -> Style("y1(t)", FontSize -> 18), 
PlotTheme -> "Detailed",
FrameLabel -> {"time", " Amplitude"}, 
LabelStyle -> {18, GrayLevel(0), 
FontFamily -> "Arial"})

plot – Plot3D of the sequence of increasing radius spheres

As mentioned in the comments, Do do not return the parcels. But why not just use Manipulate? That's what Manipulate meant.

enter the description of the image here

Manipulate[

 Module[{x, y, z, max},
  max = 10;
  ContourPlot3D[
   x^2 + y^2 + z^2 == r^2, {x, -max, max}, {y, -max, max}, {z, -max, max}, 
   PlotRange -> {{-max, max}, {-max, max}, {-max, max}}, 
   PerformanceGoal -> "Quality", 
   SphericalRegion -> True]
  ],

 {{r,5,"radius"}, 1, 10, 1, Appearance -> "Labeled",ContinuousAction->False},
 TrackedSymbols :> {r}
 ]

But if you really need static 3D plots, you can do it.

makePlot[r_] := Module[{x, y, z, max},
   max = 10;
   ContourPlot3D[
    x^2 + y^2 + z^2 == r^2, {x, -max, max}, {y, -max, max}, {z, -max, max},
    PlotRange -> {{-max, max}, {-max, max}, {-max, max}},
    PerformanceGoal -> "Quality", SphericalRegion -> True,
    PlotLabel -> Row[{"Radius ", r}]]
   ];

   Grid[Partition[Table[makePlot[r], {r, 1, 9}], 3], Frame -> All, 

Spacings -> {1, 1}]

Mathematica graphics

To update the new published requirements:

makePlot[r_] := Module[{x, y, z, max},
   Sphere[{r^2 - 1, 0, 0}, r]
   ];
tab = Table[makePlot[r], {r, 1, 4}]
Graphics3D[tab, PlotRange -> All]

Mathematica graphics