https://community.wolfram.com RSS Feed for Wolfram Community showing any discussions tagged with Biological Sciences sorted by active. https://community.wolfram.com/groups/-/m/t/3713047 ![Red hair tips electric eel in fast and slow motion: translating from P5.JS processing to Wolfram][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=ezgif-20001a6ec98fb594.gif&userId=11733 [2]: https://www.wolframcloud.com/obj/78388bcc-f070-44d3-9035-26433cf1ce85 Vitaliy Kaurov 2026-05-08T02:51:54Z https://community.wolfram.com/groups/-/m/t/3675919 **Intro** A fundamental question keeps coming up for me: If biological evolution operates in astronomically large spaces, why is search computationally tractable at all? Even a modest protein corresponds to a combinatorial space that is effectively impossible to exhaustively explore. Yet evolution does not behave like an unconstrained random search. So what makes the space navigable? **Essay** In 1859, two different perspectives on complexity emerged. Bernhard Riemann revealed deep structural order underlying the distribution of prime numbers. Charles Darwin introduced a dynamical process of variation and selection. Modern biology has successfully developed Darwin’s framework. However, something is often left implicit: the assumption that the search space is already structured in a way that makes local exploration effective. From a purely combinatorial perspective, this is problematic. Under simple assumptions (independent variation, no bias), expected search time grows exponentially with the amount of required information. In that regime, evolution would be computationally intractable. But real systems do not operate in that regime. Instead, they appear to evolve within a highly structured, constrained subspace, where: functional states are not isolated viable configurations form connected regions local mutations can traverse meaningful paths This suggests that evolution can be framed as a constrained search problem, rather than a purely stochastic process. Evolution is not merely a process acting within a space — it is a process shaped by the structure of the space it can access. This shifts the central question: What determines that accessible space? **A Minimal Computational Model** To make this concrete, consider a simple toy model. We define: a sequence space a mutation operator a constraint that restricts transitions **Basic setup** L = 20; randomSeq[] := RandomInteger[{0, 1}, L]; mutate[s_] := ReplacePart[s, RandomInteger[{1, L}] -> 1 - #] & @ s; **Fitness function** fitness[s_] := Boole[Total[s] > 12]; **Constraint energy** energy[s_] := Total[ Map[If[# === {1, 1}, 0, 1] &, Partition[s, 2, 1]] ]; **Dynamics: constrained vs unconstrained** stepConstrained[s_] := Module[{s2 = mutate[s]}, If[constraint[s, s2], s2, s] ]; stepRandom[s_] := mutate[s]; **Search experiment** findFunctional[step_, max_] := Module[ {s = randomSeq[], t = 0}, While[t < max && !TrueQ[fitness[s] == 1], s = step[s]; t++; ]; t ]; trialsConstrained = Table[ findFunctional[stepConstrained, 1000], {50} ]; trialsRandom = Table[ findFunctional[stepRandom, 1000], {50} ]; **Visualization** Histogram[ {trialsRandom, trialsConstrained}, ChartLegends -> {"Random", "Constrained"}, PlotTheme -> "Scientific", Frame -> True ] **Interpretation** In many runs, the constrained dynamics reaches functional states faster — not because the system is explicitly guided toward a target, but because the structure of the space itself has changed. Even in this minimal model, a key effect emerges: Pure random mutation behaves like unstructured search Even a simple constraint dramatically reshapes accessibility The constraint does not “guide” the system toward solutions. Instead, it reshapes the space such that functional paths become possible in the first place. **Open Questions** This raises several structural questions: - How can we formally define a constraint operator in general systems? - Can constraint-induced subspaces be measured or classified? - How does connectivity emerge in high-dimensional spaces under constraints? - Do constrained systems exhibit characteristic spectral signatures (e.g., non-random eigenvalue statistics)? **Closing Thought** The difference between intractable search and effective evolution may not lie in time or randomness — but in the geometry of the accessible space itself. Maurice Crutzen 2026-04-07T09:31:01Z https://community.wolfram.com/groups/-/m/t/122095 The latest way I have found to use my expensive math software for frivolous entertainment is this. Here's is a way to describe it. [list] [*]1000 dancers assume random positions on the dance-floor. [*]Each randomly chooses one "friend" and one "enemy". [*]At each step every dancer [list] [*]moves 0.5% closer to the centre of the floor [*]then takes a large step towards their friend [*]and a small step away from their enemy. [/list] [*]At random intervals one dancer re-chooses their friend and enemy [/list] Randomness is deliberately injected. Here is the dance... [mcode]n = 1000; r := RandomInteger[{1, n}]; f := (#/(.01 + Sqrt[#.#])) & /@ (x[[#]] - x) &; s := With[{r1 = r}, p[[r1]] = r; q[[r1]] = r]; x = RandomReal[{-1, 1}, {n, 2}]; {p, q} = RandomInteger[{1, n}, {2, n}]; Graphics[{PointSize[0.007], Dynamic[If[r < 100, s]; Point[x = 0.995 x + 0.02 f[p] - 0.01 f[q]]]}, PlotRange -> 2][/mcode] [img]/c/portal/getImageAttachment?filename=OPTfnlfrnds.gif&userId=11733[/img] Thanks to Vitaliy for posting this on my behalf, complete with animations :-) Background: I had read somewhere that macro-scale behaviour of animal swarms (think of flocks of starlings or shoals of herring) is explained by each individual following very simple rules local to their vicinity, essentially 1) try to keep up and 2) try not to collide. I started trying to play with this idea in Mathematica, but it was rather slow to identify the nearest neighbours of each particle. So I wondered what would happen if each particle acted according to the locations of two other particles, regardless of their proximity. The rule was simply to move away from one and towards the other. The contraction (x = 0.995 x) was added to prevent the particle cloud from dispersing towards infinity or drifting away from the origin. I tweaked the "towards" and "away" step sizes to strike a balance between the tendency to clump together and to spread apart (if you make the step sizes equal you get something more like a swarm of flies). With each particle's attractor and repeller fixed, the system finds a sort of dynamic equilibrium, so to keep things changing I added a rule to periodically change the attractor and repeller for one of the particles. The final adjustment was to make the "force" drop towards zero for particles at very close range. This helps to stop the formation of very tight clumps, and also prevents a division-by-zero error when a particle chooses itself as its attractor or repeller. The description of the system as a dance was an attempt to explain the swirling pattern on the screen without using mathematical language. I'd love to see what other "dances" can be created with other simple rules. Simon Woods 2013-09-11T18:31:12Z https://community.wolfram.com/groups/-/m/t/3674011 The Genetic Code as Geometry on Q_6: Hidden Mathematical Structure in the Codon Hypercube S.H. Bachani, Merlin Digital, Dubai, UAE April 2026 **Abstract** This computational exploration demonstrates how the 64 genetic codons, naturally embedded on a 6-dimensional hypercube (Q_6), reveal unexpected physical structure when annotated with ab initio quantum chemistry data. By analyzing the graph Laplacian of formation and solvation energies, we show that clinical pathogenicity in genetic mutations can be predicted from first principles without machine learning. 1. The Codon Hypercube Every codon consists of three nucleotide positions drawn from \{U, C, A, G\}. By encoding these as 2-bit values (U=00, C=01, A=10, G=11), each codon becomes a 6-bit binary string. Consequently, the 64 codons naturally occupy the vertices of Q_6, the 6-dimensional hypercube. (* Nucleotide encoding *) [span_7](start_span)nucBits = <|"U" -> 0, "C" -> 1, "A" -> 2, "G" -> 3|>;[span_7](end_span) [span_8](start_span)nucFromBits = <|0 -> "U", 1 -> "C", 2 -> "A", 3 -> "G"|>;[span_8](end_span) (* Codon to Q6 vertex *) codonToVertex[codon_String] := nucBits[StringTake[codon, {1}]] * 16 + nucBits[StringTake[codon, {2}]] * 4 + [span_9](start_span)nucBits[StringTake[codon, {3}]];[span_9](end_span) (* Q6 vertex to codon *) vertexToCodon[s_Integer] := nucFromBits[BitAnd[BitShiftRight[s, 4], 3]] <> nucFromBits[BitAnd[BitShiftRight[s, 2], 3]] <> [span_10](start_span)nucFromBits[BitAnd[s, 3]];[span_10](end_span) (* Construct Q6 *) [span_11](start_span)Q6 = HypercubeGraph[6];[span_11](end_span) Q_6 has 64 vertices and 192 edges. Each edge connects codons that differ by a single-bit mutation—representing the minimal change at one nucleotide position. 2. Formation Energies and Curvature Using standard HF/6-31G* values, we place formation energies (V_{ef}) at each vertex. The 64 codons partition into exactly 21 energy classes (20 amino acids + 1 stop signal). To measure how a codon's energy differs from its mutational neighborhood, we use the discrete Laplacian: High magnitude |\nabla^2 V| indicates a codon sits at a "peak" or "valley" where mutations cause large physicochemical shifts. Low |\nabla^2 V| indicates an energy "plateau" where mutations are tolerated. 3. Predicting Mutation Pathogenicity Analysis of 203,156 ClinVar variants reveals that the geometry of Q_6 predicts clinical outcomes: * Mean |\nabla^2 V| for Pathogenic variants: 90.7 * Mean |\nabla^2 V| for Benign variants: 40.1 Pathogenic mutations originate preferentially from high-curvature positions on the hypercube. This physical metric is orthogonal to existing tools like AlphaMissense, capturing a different physical dimension of vulnerability. 4. Solvation and Multi-Landscape Analysis A second landscape—solvation free energy (\Delta G_{solv})—reproduces experimental hydrophobicity (\rho = 0.810) without empirical fitting. The Laplacians of these two fields (\nabla^2 V_{ef} and \nabla^2 V_{solv}) are nearly independent (\rho = 0.167), representing distinct axes of "product disruption" and "folding disruption". 5. Questions for the Community * Is the genetic code a ground state? Does the standard code minimize the "frustration" (sum of energy differences across edges) compared to random reassignments on Q_6? * Why Q_6? Is there a geometric constraint that makes 6-dimensional space optimal for encoding 21 energy classes? * Quantum Hardware: This structure maps to a 6-qubit register, currently used in topologically-constrained quantum lattice architectures (US Patent 64/027,290). References * [1] Bachani, S.H. (2026). Computational framework for genomic analysis using hexagramic principles. Int. J. Phys. * [2] US Patent Application 64/027,290 (April 3, 2026). * [3] Wolfram, S. (2025). What's Special about Life? Suhail Bachani 2026-04-03T22:12:16Z https://community.wolfram.com/groups/-/m/t/3671124 ![Fireflies or nature's cellular automaton][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=4420FirefliesorNature%27sCellularAutomaton.gif&userId=20103 [2]: https://www.wolframcloud.com/obj/abfab849-1504-446c-90d3-4a5b862ab440 Kirill Vasin 2026-03-27T18:14:17Z https://community.wolfram.com/groups/-/m/t/3649858 ![enter image description here][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=5641hero.png&userId=20103 [2]: https://www.wolframcloud.com/obj/2638b19a-4d78-495a-b65d-150df2e1923a Valerie Artavia 2026-03-05T20:48:58Z https://community.wolfram.com/groups/-/m/t/3642486 ![Peppers and the heat of the nightshade: capsaicin chemistry, SHU scaling, and Solanaceae taxonomy][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Peppersandtheheatofthenightshade.png&userId=20103 [2]: https://www.wolframcloud.com/obj/718eded5-aa17-4dd5-8df7-eea1622b7a7b Gay Wilson 2026-02-20T22:16:01Z https://community.wolfram.com/groups/-/m/t/3642762 ![Modeling Ocean Plastics and Microplastic Bioaccumulation in Marine Food Webs][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=7196image.png&userId=911151 [2]: https://www.wolframcloud.com/obj/29d1e66c-401f-4cd2-baeb-77c298c257af Wolfram Education Programs 2026-02-20T18:45:33Z 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/3638608 ![Evolving cellular automata megafauna through point mutations][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=5789image.png&userId=20103 [2]: https://www.wolframcloud.com/obj/bd64452d-92b7-4317-a7fd-bb2ee51d9590 Wolfram Education Programs 2026-02-11T16:27:56Z https://community.wolfram.com/groups/-/m/t/3637839 ![enter image description here][1] ## Original ideas: - ART: https://x.com/yuruyurau/status/2017968467186799048 - ARTIST: https://x.com/yuruyurau ## Art, perception, computation New kinetic art. Rich motion via tiny math. Compression is an aspect of art. Mind connects the dots without lines; and also in time - beyond space. Artist's design is spatiotemporal - the dynamics is Intricate - time are space pattern are entangled. High visual complexity from a very short code. OLD QUESTION: How does the mind make a creature from dots? Enactivism says perception is something you do, not something that happens to you. 4E cognition puts that into four plain ideas: your mind is embodied in a body, embedded in a situation, enacted through action and perception, and can extend into tools, like a screen. This animation shows it cleanly. The code does not contain a “creature” as an object. Your visual system builds one by tracking coherent motion, binding thousands of dots into one moving agent, and using your expectations about how living things move to keep that agent stable from moment to moment. The “life” you feel is the mind doing its job: turning raw motion into a usable world. ## Original p5.JS Processing code: > a=(y=i/790,d=mag(k=(y<8?9+sin(y^9)*6:4+cos(y))*cos(i+t/4),e=y/3-13)+cos(e+t*2+i%2*4))=>point((q=y*k/5*(2+sin(d*2+y-t*4))+80)*cos(c=d/4-t/2+i%2*3)+200,q*sin(c)+d*9+60) t=0,draw=$=>{t||createCanvas(w=400,w);background(9).stroke(w,116);for(t+=PI/90,i=1e4;i--;)a()} ## Translation into Wolfram Language Compile function exactPointData = Compile[{{t, _Real}}, Table[ Module[{y, k, e, d, q, c, xCoord, yCoord, iVal}, iVal = N[i]; y = iVal/790.0; e = y/3.0 - 13.0; k = If[y < 8.0, 9.0 + 6.0 * Sin[BitXor[Floor[y], 9]], 4.0 + Cos[y] ] * Cos[iVal + t/4.0]; d = Sqrt[k^2 + e^2] + Cos[e + t*2.0 + Mod[i, 2]*4.0]; q = (y * k / 5.0) * (2.0 + Sin[d*2.0 + y - t*4.0]) + 80.0; c = d/4.0 - t/2.0 + Mod[i, 2]*3.0; xCoord = q * Cos[c] + 200.0; yCoord = -(q * Sin[c] + d*9.0 + 60.0); {xCoord, yCoord} ], {i, 9999, 0, -1} ], RuntimeOptions -> "Speed" ]; ## Collage of random frames, rotations, reflections ImageCollage[Table[ ImageCrop@ ImageRotate[#,RandomChoice[{0,Pi}]]&@ ImageReflect[#,RandomChoice[{Left,Top}]]&@ Rasterize[Graphics[ {Opacity[0.9], PointSize[.002], White,Point[exactPointData[RandomReal[8Pi]]]}, Background -> GrayLevel[0.035], (* background(9) approx 9/255 *) PlotRange -> {{40, 360}, {-390, -10}}, ImageSize -> 550 ]],6],Method->"Rows"] ![enter image description here][2] ## 3D image stack in semitransparent background Image3D[Rasterize/@frames,ViewPoint->Top,Background->Opacity[.75],ImageSize->550] ![enter image description here][3] ## 3D image stack rotation in fully transparent background Image3D[Rasterize/@frames,ColorFunction->"XRay", Background->Black,BoxRatios->{1, 1, 1},SphericalRegion->True] ![enter image description here][4] ## Animate with Manipulate function: Manipulate[ Graphics[ {Opacity[0.75], PointSize[.002], White,Point[exactPointData[t]]}, Background -> GrayLevel[0.035], PlotRange -> {{40, 360}, {-390, -10}}, ImageSize -> 550 ], {{t, 19.35, "Time"}, 19.35, 19.35+ 8 Pi,AnimationRate->.1,Appearance->"Open"} ] ![enter image description here][5] ## Animated GIF (see top image) frames=Table[ Graphics[ {Opacity[0.9], PointSize[.002], White,Point[exactPointData[t]]}, Background -> GrayLevel[0.035], (* background(9) approx 9/255 *) PlotRange -> {{40, 360}, {-390, -10}}, ImageSize -> 550 ], {t, 19.35, 19.35+ 4 Pi, 4 Pi/200.} ]; SetDirectory[NotebookDirectory[]] Export["wjelly.gif",frames,ImageSize->550,"DisplayDurations"->.03] ## 3D image stack GiF - infinity spin Be carful with CPU and RAM usage for the code below. frames=Table[ Rasterize@Graphics[ {Opacity[0.9], PointSize[.002], White,Point[exactPointData[t]]}, Background -> GrayLevel[0.035], (* background(9) approx 9/255 *) PlotRange -> {{40, 360}, {-390, -10}}, ImageSize -> 200 ], {t, 19.35, 19.35+ 4 Pi, 4 Pi/200.} ]; ClearAll[ing3D]; ing3D[d_]:=Image3D[d,ViewPoint->Top,Background->Opacity[.75],ImageSize->550] frm=ParallelTable[Rasterize[ing3D[RotateLeft[frames,k]]],{k,0,200,1}]; Export["wjelly3D.gif",frm,ImageSize->550,"DisplayDurations"->.03] ![enter image description here][6] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=wjelly2-ezgif.com-optimize.gif&userId=11733 [2]: https://community.wolfram.com//c/portal/getImageAttachment?filename=4146g4q5ergfq543gdf.jpg&userId=11733 [3]: https://community.wolfram.com//c/portal/getImageAttachment?filename=cdgwhsfdbfv.jpg&userId=11733 [4]: https://community.wolfram.com//c/portal/getImageAttachment?filename=sfd4w5wfdadsfSDF4.gif&userId=11733 [5]: https://community.wolfram.com//c/portal/getImageAttachment?filename=fg4qdsbb54.jpg&userId=11733 [6]: https://community.wolfram.com//c/portal/getImageAttachment?filename=wjelly3D-ezgif.com-optimize.gif&userId=11733 Vitaliy Kaurov 2026-02-10T06:13:14Z https://community.wolfram.com/groups/-/m/t/3607816 ![Exploring Hydrogen Bonding Patterns in Proteins][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=hBondGraph.png&userId=3607438 [2]: https://www.wolframcloud.com/obj/3b73030e-7416-4f1a-b858-751efa05c461 Christoph Steck 2026-01-15T21:48:27Z https://community.wolfram.com/groups/-/m/t/3607149 ![Percolation in fitness-neutral sets in the minimal model for biological evolution][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=merged.png&userId=20103 [2]: https://www.wolframcloud.com/obj/1f95bf03-2555-4bb3-93ad-a3c7e1deba30 Rami Zakh 2026-01-15T18:35:21Z https://community.wolfram.com/groups/-/m/t/3606767 ![This image explains that the suspension of nanoparticles in the base fluid/conventional heat carrier fluids produces nanofluid--- an improved heat carrier fluid ][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=DefinitionofNanofluid.png&userId=3572506 [2]: https://www.wolframcloud.com/obj/d174bbab-054d-4f2d-a8fa-6f83a5893113 Lateefat Aselebe 2026-01-15T02:13:16Z https://community.wolfram.com/groups/-/m/t/3597063 &[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/6c5bed41-b6e1-4849-ae85-8f7586c25b93 Hee-Young Shin 2025-12-25T21:26:33Z https://community.wolfram.com/groups/-/m/t/3597072 &[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/31b8731c-e1a6-4ccc-a5ec-7fcd62cd6b50 Hee-Young Shin 2025-12-25T21:27:55Z https://community.wolfram.com/groups/-/m/t/3586632 I've developed two theoretical frameworks that extend Wolfram's work on computational irreducibility and Class 4 systems to foundational problems in philosophy of mind. [CIFW (Computational Irreducibility and Free Will)][1] argues that the phenomenology of free will, the felt sense that multiple futures are genuinely open during deliberation, corresponds directly to Class 4 computational dynamics in neural decision-making. The subjective experience of freedom isn't illusion, but the epistemic signature of computationally irreducible processes where outcomes cannot be predicted without step-by-step execution. [CIPC (Computational Irreducibility and Phenomenal Consciousness)][2] proposes that qualia emerge necessarily when systems exhibit: (1) Class 4 dynamics, (2) self-modeling, (3) environmental modeling, (4) information integration, and (5) operation under uncertainty. Consciousness isn't something added to computation, it's what Class 4 self-referential computation is like from the system's own perspective. Both papers make testable predictions via EEG complexity measures and comparative neuroscience, and both dissolve rather than solve their respective philosophical problems by revealing them as category errors. I would be honored if the community could give their opinion on my ideas. [1]: https://osf.io/preprints/psyarxiv/e5ajp [2]: https://zenodo.org/records/17834417 Rafael Almeida Reis 2025-12-06T10:44:02Z https://community.wolfram.com/groups/-/m/t/3585501 ![A school of swimming jellyfish: trigonometric and boolean rendering ][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=fishyjelly2-ezgif.com-optimize.gif&userId=11733 [2]: https://www.wolframcloud.com/obj/1650c140-fea8-42bf-ac77-ba7cd9a0a725 Vitaliy Kaurov 2025-12-04T11:45:25Z https://community.wolfram.com/groups/-/m/t/3582366 ![A framework for modelling gene regulation which accommodates non-equilibrium mechanisms][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Aframeworkformodellinggeneregulationwhichaccommodatesnon-equilibriummechanisms2.png&userId=20103 [2]: https://www.wolframcloud.com/obj/419d1e91-b71e-43f5-9c79-c7ae37ccac97 Jeremy Gunawardena 2025-11-26T21:06:30Z https://community.wolfram.com/groups/-/m/t/3574743 ![Truss structure optimization using a genetic algorithm][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Trussstructureoptimizationusingageneticalgorithm.png&userId=20103 [2]: https://www.wolframcloud.com/obj/e038db24-853f-492a-bebf-ebd6e4526092 Diego Alves 2025-11-13T17:11:12Z