https://community.wolfram.com RSS Feed for Wolfram Community showing any discussions tagged with Dynamic Interactivity sorted by active. https://community.wolfram.com/groups/-/m/t/3656731 &[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/545ac7e4-f815-43fb-9d0f-33d85e0f5e2d Brian Beckman 2026-03-10T23:44:24Z https://community.wolfram.com/groups/-/m/t/3651250 ![Computational dynamics of the classical and perturbed circular restricted three-body problem][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=10346hero.png&userId=20103 [2]: https://www.wolframcloud.com/obj/f37e309d-f41e-45e5-a952-bb2953a400c4 Akram Masoud 2026-03-06T16:49:26Z https://community.wolfram.com/groups/-/m/t/3644671 [![Self-directed learning with notebooks: students' experiences in a chemical thermodynamics exercise][1]][2] &[Wolfram Notebook][3] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Self-directedlearningwithnotebooksstudents%E2%80%99experiencesinachemicalthermodynamicsexerc.jpg&userId=20103 [2]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Self-directedlearningwithnotebooksstudents%E2%80%99experiencesinachemicalthermodynamicsexerc.jpg&userId=20103 [3]: https://www.wolframcloud.com/obj/c863fe35-3afe-4103-b447-ca6e6feb3f4c Michael Haring 2026-02-24T19:19:08Z https://community.wolfram.com/groups/-/m/t/3642901 &[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/f58b42ce-750f-48f1-9529-f640d895b1cc Michael Rogers 2026-02-21T02:40:03Z https://community.wolfram.com/groups/-/m/t/3641221 ![Modeling Below-the-Knee Prosthetics using FEM and SLIP Dynamics][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=5977image.png&userId=911151 [2]: https://www.wolframcloud.com/obj/d0eba471-b424-4c38-a404-ed4e94a5dd7b Wolfram Education Programs 2026-02-17T15:45:48Z https://community.wolfram.com/groups/-/m/t/3629162 ![[WWS26] Birdwatching: A tale of S combinator arithmetic][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=birdy.jpg&userId=2851656 [2]: https://www.wolframcloud.com/obj/7a744e7c-97b0-426e-8b1e-fa990fd0ae47 Russell Martinez 2026-01-27T18:19:34Z https://community.wolfram.com/groups/-/m/t/3622456 ![Mathematical Games 37: Two Phi Psi Chi Rho (2 φ ψ χ ρ)][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=MathematicalGames37TwoPhiPsiChiRho2%CF%86%CF%88%CF%87%CF%81.png&userId=20103 [2]: https://www.wolframcloud.com/obj/7c4c0ff2-3911-4c19-b956-a776fafc4040 Ed Pegg 2026-01-22T16:59:42Z https://community.wolfram.com/groups/-/m/t/3606056 I have a problem when using DynamicModule to represent a dynamical system of the type State(t)->F(State(t+1)). In the attached code, the animation does not start. Could any one tell me why? Thanks. &[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/a199f22d-e876-4d61-bb62-2b4c4d2cf7da Christian Mullon 2026-01-14T12:07:51Z https://community.wolfram.com/groups/-/m/t/3602119 &[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/59e2a8f6-2b99-4f93-87ff-aa41cede2392 Hee-Young Shin 2026-01-06T17:23:41Z https://community.wolfram.com/groups/-/m/t/3600562 &[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/6885767e-1ad6-48a8-b7f8-3ea83983bd15 Hee-Young Shin 2026-01-03T19:53:35Z https://community.wolfram.com/groups/-/m/t/3590761 &[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/eb895976-f39e-4f04-8dbc-21fa665b3b90 Hee-Young Shin 2025-12-15T00:19:32Z https://community.wolfram.com/groups/-/m/t/3585466 [![Qubits explained: Bloch sphere, SU(2) rotations & measurements — Guided, computation-first narrative][1]][2] &[Wolfram Notebook][3] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=1515QubitsExplainedBlochSphere,SU%282%29Rotations,andMeasurements.png&userId=20103 [2]: https://community.wolfram.com//c/portal/getImageAttachment?filename=1515QubitsExplainedBlochSphere,SU%282%29Rotations,andMeasurements.png&userId=20103 [3]: https://www.wolframcloud.com/obj/343c8c4d-7d34-4b06-bcfc-6a06e4f75a83 Mohammad Bahrami 2025-12-04T00:03:54Z https://community.wolfram.com/groups/-/m/t/3578212 ![Wolfram & Raspberry Pi 5 — Part 2: compilation and mathematical visualization][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Complilationandmathematicalvisualization.png&userId=20103 [2]: https://www.wolframcloud.com/obj/79e1b917-7c75-49f9-8759-e92375c40c34 Bart ter Haar Romeny 2025-11-19T19:56:59Z https://community.wolfram.com/groups/-/m/t/3574993 I have a small DynamicModule that displays a slider for x and the result of evaluating a function f[x]. The following code works as desired: DynamicModule[{f, x = 5}, f[x_] := {x, Sqrt[x]}; Column[{ Slider[Dynamic@x, {0, 25, 1}], Dynamic@f[x] }] ] ![enter image description here][1] Now I want to store the results of f[x] in two variables arg and val for later use. The following code works, but it throws a Set::shape error during the assignment of the result, and the variables arg and val are not set. DynamicModule[{f, x = 5, arg, val}, f[x_] := {x, Sqrt[x]}; Column[{ Slider[Dynamic@x, {0, 25, 1}], {arg, val} = Dynamic@f[x], Row[{"{arg,val} = ", Dynamic@{arg, val}}] }] ] ![enter image description here][2] *The reason for the error is that Dynamic@f[x] is an object and not a list.* **How can I fix this problem?** Perhaps with something like Dynamic[f[x], someFunction] instead of {arg,val}=Dynamic[f[x]], where someFunction assigns arg and val? [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2025-11-14182646.jpg&userId=890153 [2]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2025-11-14183123.jpg&userId=890153 Werner Geiger 2025-11-14T17:33:56Z https://community.wolfram.com/groups/-/m/t/3574670 &[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/d8e5d5cd-83af-487b-9c48-d4a82ef214f1 Werner Geiger 2025-11-13T21:41:30Z https://community.wolfram.com/groups/-/m/t/3061868 I have two notebooks (tiltg.nb and tiltb.nb, attached) which, when viewed by the desktop notebook interface, are identical. However, they exhibit different behaviors when uploaded to the Wolfram Cloud. The first shows the output cell produced by a closed Manipulate cell. The second shows an empty Manipulate panel colored pink, with no explanation of why it failed. When I explicitly open and evaluate the closed cell containing the Manipulate in the second, it produces the desired output cell. I made a textual comparison of the two notebooks. There are some expected differences including Cell Change Times, Expression UUID, CellLabel, CellContext, NotebookDataLength, NotebookOptionsPosition, NotebookOutlinePosition, and CellTagsIndexPosition. The only suspicious difference is that the working version has an Initialization section containing lines like the following: Initialization:>{ Attributes[$CellContext`center$] = {Temporary}, ... Attributes[$CellContext`square$] = {Temporary}} for each of the Manipulate's Module's local Symbols. I assume these lines are somehow generated when the Manipulate is evaluated, and I don't know why the working version has them and the erroneous version doesn't. My questions are the following: - Could these Attributes lines explain why the first notebook worked and the second didn't? - If not, could you suggest what might be causing the failure? - How/why do these Attributes lines (and the Initialization section) get generated? - What can I do to ensure that the second version of the notebook has them? - What is the $CellContext context, and what does {Temporary} signify? Background: This particular Manipulate has been used successfully on the desktop for several years. I want to include the Manipulate as part of a larger notebook in the cloud, and I don't want the end user to confront a pink panel. Locally, I am running on a MacBook M2, with Sonoma 14.0 and Mathematica 13.2.1.0. I am not aware of having done any specific customization to my cloud account. The Graphics.wl library (referenced in the initialization cell) is a mature collection of function definitions that works successfully on both the desktop and the cloud. I have attached the relevant functions in a notebook (graphics.nb). Spencer Rugaber 2023-11-08T18:24:28Z https://community.wolfram.com/groups/-/m/t/3567201 &[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/1c7fc3d5-95a6-4b0b-becf-0afd3aeaf83d Daniel Carvalho 2025-10-29T02:20:39Z https://community.wolfram.com/groups/-/m/t/3563534 In this preliminary post I introduce the idea of dynamical Transformation Functions, that is, the situation where the Transformation Matrices have functions rather than numbers as entries. I apply this specifically in the case of even (direct) isometries of real 3-space. I introduce DITF format which is independent of the construction of the transformation function. I give a geometrical interpretation which shows motion in space not only the position but also the orientation of the object. Several examples are given. Barry H Dayton 2025-10-22T00:17:13Z https://community.wolfram.com/groups/-/m/t/3558592 ![Wolfram & Raspberry Pi 5: Complete STEM applications, advanced visualizations & GPIO sensor support][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=STEMstudent%27sdream.png&userId=20103 [2]: https://www.wolframcloud.com/obj/37751904-8fa2-44eb-a492-7983fdc9dcd8 Bart ter Haar Romeny 2025-10-09T17:30:45Z https://community.wolfram.com/groups/-/m/t/3554402 ![Recreation of World of Goo or bridge construction game with WLJS][1] Based on original article: https://wljs.io/blog/2025/08/22/goo/ Here we shall try to model a system of interconnected bonds using the Verlet method. Then, we'll add some visuals to make it feel like a game. #Motion Equations The system of connected points must obey Newton's laws and kinematic equations as well. To integrate them in real-time, Euler's method, RK (Runge-Kutta), or Verlet methods can be used. We will go for the Verlet method since it will be easier to apply constraints of the bonds in the future: $$x_{n+1} = 2x_n - x_{n-1} + \frac{f_n}{m} \delta t^2$$ We can try to apply it for the simples case, when $\mathbf{f}_n = -m\mathbf{x} / |\mathbf{x}|^4$ is sort of a gravity force caused by a red star in the center estimateX[n_Integer, initialV_ : 0.01] := FixedPoint[ Function[ x, {2 x[[1]] - x[[2]] - 0.001 ((x[[1]])/(Power[Norm[x[[1]]], 4])), x[[1]], x[[2]]}], {{-1.0, 2 initialV 0.01}, {-1.0, initialV 0.01}, {-1.0, 0}}, n]; Now let's plot our solutions for different initial conditions: Table[{v, Table[estimateX[n, v][[1]], {n, 1, 100}]}, {v,0,4}]; % // Transpose; ListLinePlot[ %[[2]] , PlotStyle -> AbsoluteDashing[{3}] , PlotRange -> 2{{-1,1}, {-1,1}} , PlotLegends -> (StringTemplate["v = ``"][#]&/@ %[[1]]) , Epilog -> {Red, Disk[{0,0}, 0.1]} , Frame -> True , AspectRatio -> 1 ] ![enter image description here][2] *The case of v=3 must be related to the orbital velocity of a star* To see it animated we should repeat the calculations for every frame With[{initialV = 3.0}, Module[{point = {{-1.0, 2 initialV 0.01}, {-1.0, initialV 0.01}, {-1.0, 0}}}, EventHandler["frameXXX", Function[Null, point[[3]] = point[[2]]; point[[2]] = point[[1]]; point[[1]] = 2 point[[2]] - point[[3]] - ((point[[1]])/(Power[Norm[point[[1]]], 4])) 0.001; point = point; (*to trigger an update*)]]; Graphics[{Point[point // Offload], AnimationFrameListener[point // Offload, "Event" -> "frameXXX"]}, PlotRange -> 2 {{-1, 1}, {-1, 1}}, Epilog -> {Red, Disk[{0, 0}, 0.1]}, AspectRatio -> 1]]] ![enter image description here][3] #Constraints Algorithm The simplest and well-known approach for solving the bonds problem is approximating it with springs with finite or infinite stiffness. As it follows from [Wikipedia article][4]: > ![enter image description here][5] where s is an effective stiffness constant: s=1 represents an infinitely stiff spring (hard bond), and s<1 represents a soft bond. > Verlet integration is useful because it directly relates the force to the position, rather than solving the problem using velocities. Note: Constraints Algorithm is applied on the vertices **after** Verlet integration has been performed. Let's draft a function, that takes the following arguments and process the data efficiently: - list of vertices - list of indices of fixed vertices - list of bonds: - index A - index B - initial length - stiffness And it should output a new list of vertices: processVertices[vertices_List, fixed_List, bonds_List] := Module[{coords = vertices[[1]], coords2 = vertices[[2]], coords3 = vertices[[3]]}, Do[coords3 = coords2; coords2 = coords; Module[{integrated = 2 coords2 - coords3 + Table[{0, -1}, Length[coords]] 0.001}, MapThread[ Function[{i, j, l, s}, With[{d = integrated[[i]] - integrated[[j]]}, {norm = Norm[d]}, {m = 0.5 s Min[(l/(norm + 0.001) - 1), 0.1] (*avoid blowing up the system*)}, integrated[[i]] += m d; integrated[[j]] -= m d;]], RandomSample[bonds] // Transpose]; Map[Function[index, integrated[[index]] = coords[[index]];], fixed]; coords = integrated;];, {2 5}]; {coords, coords2, coords3}] Note: For the stability it is recommended to apply constraints in random order Let us try it on some basic example: bridge = Join @@ Table[{{i, 75}, {i + 5, 55}}, {i, 1, 100, 10}]; bonds = Join[Table[{i, i + 1}, {i, 1, Length[bridge] - 1, 2}], Table[{i, i + 2}, {i, 1, Length[bridge] - 2, 2}], Table[{i + 1, i + 3}, {i, 1, Length[bridge] - 3, 2}]]; bonds = Map[ Join[#, {Norm[bridge[[#[[1]]]] - bridge[[#[[2]]]]], 0.7} // N] &, bonds]; plotBridge[bridge_] := Graphics[{MapThread[{bridge[[#1]], bridge[[#2]]} &, bonds // Transpose] // Line, Point[bridge], ColorData[97][6], MapIndexed[Text[#2[[1]], #1] &, bridge]}, PlotRange -> {{0, 100}, {0, 100}}, "Controls" -> False]; plotBridge[bridge] ![enter image description here][7] Let's run the simulation for a few iterations and plot the final result, while keeping [1,2] vertices fixed at the original positions Module[{bridgeState = {bridge, bridge, bridge}}, Do[ bridgeState = processVertices[bridgeState, {1,2,19,20}, bonds]; , {10}]; Show[plotBridge[bridge], plotBridge[bridgeState[[1]]]] ] ![enter image description here][8] Great! At least it did not collapse :) It would be great to see it live. For this we apply the same strategy with `Offload` technique Module[{bridgeState, lines, points, frame = CreateUUID[]}, EventHandler[frame, Function[Null, bridgeState = processVertices[bridgeState, {1, 2, 19, 20}, bonds]; lines = MapThread[{bridgeState[[1, #1]], bridgeState[[1, #2]]} &, bonds // Transpose];]]; bridgeState = {bridge, bridge, bridge}; lines = MapThread[{bridgeState[[1, #1]], bridgeState[[1, #2]]} &, bonds // Transpose]; points = bridge; Show[plotBridge[bridge], Graphics[{ColorData[97][9], Point[points // Offload], Line[lines // Offload], AnimationFrameListener[lines // Offload, "Event" -> frame]}]]] ![enter image description here][10] #Preparing Graphics The original inspiration was a puzzle video game developed and published by 2D Boy - **The World of Goo**. It was first released in 2008. In the game, players must use balls of goo to build structures, such as bridges, towers and etc. We start from the background, and add some blur to it: background = Blur[ ![enter image description here][11] , 10]; clouds = { ![enter image description here][12], ![enter image description here][13] }; #Rendering Rendering the scene using retained mode with pure raster graphics is more efficient, especially when applying special effects. For this reason we use Javascript Canvas API, which is mapped 1:1 to `Canvas2D` library Needs["Canvas2D`"->"ctx`"] // Quiet; Let's define a helper function for rendering bonds: drawBonds[context_, vert_, edges_, fixed_, {width_, height_}] := (ctx`BeginPath[context]; ctx`SetLineWidth[context, 4]; ctx`SetStrokeStyle[context, "#2C6C75"]; Do[ctx`MoveTo[context, {0, height} - {-1, 1} vert[[p[[1]]]]]; ctx`LineTo[context, {0, height} - {-1, 1} vert[[p[[2]]]]];, {p, edges}]; ctx`Stroke[context]; ctx`SetFillStyle[context, "#1C4E28"]; (ctx`BeginPath[context]; ctx`Arc[context, {0, height} - {-1, 1} #, 6, 0, 2.0 Pi]; ctx`Fill[context];) & /@ vert; ctx`SetFillStyle[context, RGBColor[0.9, 0.4, 0.4] // Darker]; (ctx`BeginPath[context]; ctx`Arc[context, {0, height} - {-1, 1} vert[[#]], 4, 0, 2.0 Pi]; ctx`Fill[context];) & /@ fixed;); Here we use the same bridge section and render it using our new raster renderer: Module[{ ctx = ctx`Canvas2D[] }, drawBonds[ctx, 5 bridge, bonds, {1,2,19,20}, {500,500}]; ctx`Dispatch[ctx]; Image[ctx, ImageResolution->{500,500}] ] ![enter image description here][14] As a basic visual effect, we can add a trailing effect to the cursor, similar to how it was done in the original game (to some extent): drawPointer[context_, trail_, edges_, {width_, height_}] := ( ctx`BeginPath[context]; ctx`SetLineWidth[context, 2]; ctx`SetStrokeStyle[context, RGBColor[0.4, 0.6, 0.9]//Darker]; Do[ ctx`MoveTo[context, {0, height} - {-1, 1} t[[1]]]; ctx`LineTo[context, {0, height} - {-1, 1} t[[2]]]; , {t, edges}]; ctx`Stroke[context]; ctx`SetFillStyle[context, RGBColor[0.4, 0.9, 0.6]//Darker]; Do[ ctx`BeginPath[context]; ctx`Arc[context, {0, height} - {-1, 1} trail[[i]], 6.0/i, 0, 2.0 Pi]; ctx`Fill[context]; , {i, Length[trail]}]; ); - Module[{ ctx = ctx`Canvas2D[], trail = Table[{0,0}, {10}], frame = CreateUUID[], target = {0,0}, state = Table[bridge // N, {3}] }, EventHandler[frame, Function[Null, ctx`ClearRect[ctx, {0,0}, {500,500}]; drawBonds[ctx, 5 state[[1]], bonds, {1,2,19,20}, {500,500}]; drawPointer[ctx, trail, {}, {500,500}]; ctx`Dispatch[ctx]; trail = RotateRight[trail, 1]; trail[[1]] = target; state = processVertices[state, {1,2,19,20}, bonds]; ]]; EventHandler[Image[ctx, ImageResolution->{500,500}, Epilog->AnimationFrameListener[ctx, "Event"->frame] ], { "mousemove"->Function[xy, target = {0,500} + {1,-1} xy; ]}] ] #Utils For adding more bonds to the structure of a bridge, we need to find the shortest links (maximum 2) to the cursor position. Here is a little function for this purpose: findConnections[vertx_, p_, th_: 2.0] := With[{a = MapIndexed[Function[{val, i}, With[{n = Norm[p - val]}, If[n < th, {i[[1]], n}, Nothing]]], vertx]}, If[Length[a] == 0, {}, If[Length[a] > 2, TakeSmallestBy[a, Function[v, v[[2]]], 2], a][[All, 1]]]] It is far from the optimal solution, since it naively checks all vertices available. #Wrapping up As the last step, we add a click listener to append new vertices and bonds to the system. For the visuals, we also add a background image and moving clouds in a simple linear pattern: With[{ frame = CreateUUID[], ctx = ctx`Canvas2D[], fixed = NotebookStore["contemporaneously-be4"] }, Module[{ p, pointer, trail, target, nearbyVertices, bonds, offset, targetOffset, cloudsPos, cloudsImages }, p = NotebookStore["audience-36d"]; bonds = NotebookStore["huckster-6b8"]; nearbyVertices = {}; cloudsPos = NotebookStore["circumvention-9f5"]; cloudsImages = RandomChoice[clouds, 5]; pointer = {250,250}; offset = 0.0; targetOffset = -150; target = pointer; trail = Table[pointer, {10}]; EventHandler[frame, Function[Null, (* clear and translate the screen buffer *) ctx`ClearRect[ctx, {0,0}, {500,500}]; ctx`Translate[ctx, {0, offset}]; (* background *) ctx`DrawImage[ctx, background, {0,0}]; MapThread[ctx`DrawImage[ctx, #1, #2]&, {cloudsImages, cloudsPos}]; (* draw bridge *) drawBonds[ctx, p[[1]], bonds, fixed, {500,500}]; (* draw a cursor *) drawPointer[ctx, trail, {trail[[1]], p[[1, #]]} &/@ nearbyVertices, {500,500}]; (* reset transformation and flip the buffers *) ctx`Translate[ctx, {0, -offset}]; ctx`Dispatch[ctx]; (* trail computations *) pointer = 0.35 (target + {0,1} offset) + 0.65 pointer; trail = RotateRight[trail, 1]; trail[[1]] = pointer; (* animation of clouds *) cloudsPos = Map[If[#[[1]] > 500, {-150, #[[2]]}, # + {1,0}]&, cloudsPos]; (* camera animation *) If[target[[2]] < 100 && targetOffset > -200, targetOffset-=6.0]; If[target[[2]] > 500-100 && targetOffset < 0, targetOffset+=6.0]; offset = offset + 0.1 (targetOffset - offset); (* perform Verlet *) p = processVertices[p, fixed, bonds]; ]]; EventHandler[Image[ctx, ImageResolution->{500,500}, Epilog->{ AnimationFrameListener[ctx, "Event"->frame] }], { "click" -> Function[xy, p[[1]] = Append[p[[1]], pointer]; p[[2]] = Append[p[[2]], pointer]; p[[3]] = Append[p[[3]], pointer]; With[{length = Length[p[[1]]]}, bonds = Join[bonds, Table[ {length, i, Norm[pointer - p[[1, i]]], 0.3} , {i, nearbyVertices}]]; ]; ], "mousemove" -> Function[xy, target = {0, 500} - {-1, 1} xy; (* scan for vertices near the cursor *) nearbyVertices = findConnections[p[[1]], pointer, 60]; ] }] ]] This wasn't that hard, was it? It is amazing how powerful Wolfram Language becomes once bridged with web-tech sandbox tools &[Embedded Video][15] Note: If you are reading this from a web page and not from the WLJS Notebook: Some resources were kept within the notebook storage. Download the original notebook from the heading section to have all images and precalculated vertices. [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=world_of_goo2-cc9f5a7ba0a7819e544b1825a7054c5b%281%29.gif&userId=20103 [2]: https://community.wolfram.com//c/portal/getImageAttachment?filename=fig1.png&userId=20103 [3]: https://community.wolfram.com//c/portal/getImageAttachment?filename=1623Fig2_3.gif&userId=20103 [4]: https://en.wikipedia.org/wiki/Verlet_integration [5]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Fig3.png&userId=20103 [6]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Fig3.jpg&userId=20103 [7]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Fig4.png&userId=20103 [8]: https://community.wolfram.com//c/portal/getImageAttachment?filename=8936Fig5.png&userId=20103 [9]: https://community.wolfram.com//c/portal/getImageAttachment?filename=fig1.png&userId=20103 [10]: https://community.wolfram.com//c/portal/getImageAttachment?filename=2638Fig6.gif&userId=20103 [11]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Fig7.png&userId=20103 [12]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Fig8.png&userId=20103 [13]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Fig9.png&userId=20103 [14]: https://community.wolfram.com//c/portal/getImageAttachment?filename=10912Fig10.png&userId=20103 [15]: https://www.wolframcloud.com/obj/6b15b219-367d-4064-a1fb-70234b202185 Kirill Vasin 2025-10-02T16:13:59Z