# Rheotomic Surface, how? **URL:** \ **Category:** Geometry\ **Created:** [January 23, 2023, 6:19pm UTC](https://forum.dynamobim.com/t/rheotomic-surface-how/85245 "2023-01-23T18:19:38Z")\ **Posts on this page:** 8\ **Page:** 1
**Author:** ![Draxl\_Andreas](https://sea2.discourse-cdn.com/flex022/user_avatar/forum.dynamobim.com/draxl_andreas/32/145744_2.png) [@Draxl\_Andreas](https://forum.dynamobim.com/u/Draxl_Andreas)\ **Post date:** [January 23, 2023, 6:19pm UTC](https://forum.dynamobim.com/t/rheotomic-surface-how/85245/1 "2023-01-23T18:19:38Z")
Hello, i got hypnotized by these forms? is there anything to built up this in dynamo ? or placing families based on that šŸ™‚ > **[Rheotomic Surfaces](https://spacesymmetrystructure.wordpress.com/rheotomic-surfaces/)** > > These are Rheotomic Surfaces ā€“ from the Greek Rheo ā€“ flow and Tomos ā€“ cut or section (as in tomography) The horizontal sections of these surfaces correspond to the moving equipotential lines of a 2ā€¦ KR Andreas ---
**Author:** ![christian.stan](https://sea2.discourse-cdn.com/flex022/user_avatar/forum.dynamobim.com/christian.stan/32/166296_2.png) [@christian.stan](https://forum.dynamobim.com/u/christian.stan)\ **Post date:** [January 23, 2023, 6:28pm UTC](https://forum.dynamobim.com/t/rheotomic-surface-how/85245/2 "2023-01-23T18:28:42Z")
Hi, you looked on the site (there is his address on his file) of Mr. Vikram Mr. Marcel must have leads too I think, he seems a fan of geometric objects cordially christian.stan ---
**Author:** ![Draxl\_Andreas](https://sea2.discourse-cdn.com/flex022/user_avatar/forum.dynamobim.com/draxl_andreas/32/145744_2.png) [@Draxl\_Andreas](https://forum.dynamobim.com/u/Draxl_Andreas)\ **Post date:** [January 23, 2023, 6:30pm UTC](https://forum.dynamobim.com/t/rheotomic-surface-how/85245/3 "2023-01-23T18:30:44Z")
@christian.stan , so i ā€œawakeā€ them to this topic šŸ˜‰ @Vikram_Subbaiah @Marcel_Rijsmus ---
**Author:** ![Marcel\_Rijsmus](https://sea2.discourse-cdn.com/flex022/user_avatar/forum.dynamobim.com/marcel_rijsmus/32/8539_2.png) [@Marcel\_Rijsmus](https://forum.dynamobim.com/u/Marcel_Rijsmus)\ **Post date:** [January 23, 2023, 7:33pm UTC](https://forum.dynamobim.com/t/rheotomic-surface-how/85245/4 "2023-01-23T19:33:03Z")
Let me sleep on it šŸ˜„ No ,seriously iā€™ve moved onwards since. Maybe @Vikram_Subbaiah can be of assistance ---
**Author:** ![christian.stan](https://sea2.discourse-cdn.com/flex022/user_avatar/forum.dynamobim.com/christian.stan/32/166296_2.png) [@christian.stan](https://forum.dynamobim.com/u/christian.stan)\ **Post date:** [January 23, 2023, 8:29pm UTC](https://forum.dynamobim.com/t/rheotomic-surface-how/85245/5 "2023-01-23T20:29:04Z")
Here is a surface I donā€™t know if it comes within the prerogatives, you can add a little movement to the cylinder ![Capture dā€™Ć©cran 2023-01-23 212632](https://us1.discourse-cdn.com/flex022/uploads/dynamobim/original/3X/a/6/a628a1c6b9046b77b873a9c70986880dc73ffe21.jpeg) [23 janvier funny Draxl.dyn](https://forum.dynamobim.com/uploads/short-url/n5CObiuYl42YY7o9vNSLDvFmpfX.dyn) (29.1 KB) cordially christian.stan ---
**Author:** ![solamour](https://sea2.discourse-cdn.com/flex022/user_avatar/forum.dynamobim.com/solamour/32/153516_2.png) [@solamour](https://forum.dynamobim.com/u/solamour)\ **Post date:** [January 23, 2023, 9:24pm UTC](https://forum.dynamobim.com/t/rheotomic-surface-how/85245/6 "2023-01-23T21:24:52Z")
Not Rheotomic, but this thread has similar things šŸ˜ƒ > [@Organic Geometry Creation](https://forum.dynamobim.com/t/organic-geometry-creation/23154/5): > > its all about math, that is every shape and curve has a specific equation or combinations of multi equations. if you want to draw this on dynamo , you have to draw the basic zigzagged line which have basically sinusoidal shape then turn them to solid with specific height and copy it to layers, every layer has itā€™s own values and constants ā€¦etc. itā€™s need some efforts indeed. good luck ---
**Author:** ![leonard.moelders](https://sea2.discourse-cdn.com/flex022/user_avatar/forum.dynamobim.com/leonard.moelders/32/108216_2.png) [@leonard.moelders](https://forum.dynamobim.com/u/leonard.moelders)\ **Post date:** [January 24, 2023, 8:23am UTC](https://forum.dynamobim.com/t/rheotomic-surface-how/85245/7 "2023-01-24T08:23:01Z")
Hi @Draxl_Andreas you could have a look at this grasshopper script if you have access to rhino: > **[Rheotomic surfaces and flowline generation tool](https://www.grasshopper3d.com/profiles/blogs/rheotomic-surfaces-and-flowline-generation-tool)** > > Around 3 years ago I wrote an essay on my blog about what I called rheotomic surfacesĀ - a type of surfaceĀ I had developedĀ related to fluid flow and electrostaā€¦ If you have, but havenā€™t worked with grasshoppoer yet: Itā€™s quite similar to dynamo and you should have no problem in analysing how the script works. Here is a demo video of the author using his script: https://player.vimeo.com/video/37060860?h=05ab80bcbd&app_id=122963 ---
**Author:** ![Draxl\_Andreas](https://sea2.discourse-cdn.com/flex022/user_avatar/forum.dynamobim.com/draxl_andreas/32/145744_2.png) [@Draxl\_Andreas](https://forum.dynamobim.com/u/Draxl_Andreas)\ **Post date:** [January 25, 2023, 8:30pm UTC](https://forum.dynamobim.com/t/rheotomic-surface-how/85245/8 "2023-01-25T20:30:15Z")
@christian.stan @solamour @Marcel_Rijsmus @leonard.moelders , it is fake but funny ā€¦ i found something to the Dyole function ![image](https://us1.discourse-cdn.com/flex022/uploads/dynamobim/original/3X/b/2/b2541d05e86b01a3a3ff3554219fb8fac5606248.jpeg) thats exposed to the grasshopper graph as pythoncodeā€¦ ```auto #Seghier Mohamed Abdelaziz - 2021 import Rhino.Geometry as rg import ghpythonlib.components as ghc import math pow = math.pow sin = math.sin cos = math.cos pi = math.pi sqrt = math.sqrt q = p*n def prop(z,t,p,q): w = pow(z,p/q) s = (p*t+2*pi)/q v = [w,s] return v def _d(z,t,p,q): w = pow(z,p/q) s = (p*t+2*pi)/q v = pow(z*cos(t)-w*cos(s),2)+pow(z*sin(t)-w*sin(s),2) return v def ddz_d(z,t,p,q): w = pow(z,p/q) s = (p*t+2*pi)/q ddz_w = (p/q)*pow(z,(p-q)/q) v = 2*(w*cos(s) - z*cos(t))*(ddz_w*cos(s) - cos(t))+ 2*(w*sin(s) - z*sin(t))*(ddz_w*sin(s) - sin(t)) return v def ddt_d(z,t, p,q): w = pow(z, p/q) s = (p*t + 2*pi)/q dds_t = (p/q) v = 2*( z*cos(t) - w*cos(s) )*( -z*sin(t) + w*sin(s)*dds_t )+ 2*( z*sin(t) - w*sin(s) )*( z*cos(t) - w*cos(s)*dds_t ) return v def _s(z,t, p,q): v = pow(z + pow(z, p/q), 2) return v def ddz_s(z,t, p,q): w = pow(z, p/q) ddz_w = (p/q)*pow(z, (p-q)/q) v = 2*(w+z)*(ddz_w+1) return v def _r(z,t, p,q): v = _d(z,t,p,q) / _s(z,t,p,q) return v def ddz_r(z,t, p,q): v = (ddz_d(z,t,p,q) * _s(z,t,p,q) - _d(z,t,p,q) * ddz_s(z,t,p,q)) / pow( _s(z,t,p,q), 2 ) return v def ddt_r(z,t, p,q): v = (ddt_d(z,t,p,q) * _s(z,t,p,q)) / pow( _s(z,t,p,q), 2 ) return v #------------------------------------------------------- def _f(z, t): return _r(z,t,0,1) - _r(z,t,p,q) def ddz_f(z, t): return ddz_r(z,t,0,1) - ddz_r(z,t,p,q) def ddt_f(z, t): return ddt_r(z,t,0,1) - ddt_r(z,t,p,q) def _g(z, t): return _r(z,t,0,1) - _r(pow(z, p/q), (p*t + 2*pi)/q, 0 ,1) def ddz_g(z, t): return ddz_r(z,t,0,1) - ddz_r(pow(z, p/q), (p*t + 2*pi)/q, 0,1) * (p/q)*pow(z, (p-q)/q) def ddt_g(z, t): return ddt_r(z,t,0,1) - ddt_r(pow(z, p/q), (p*t + 2*pi)/q, 0,1) * (p/q) #------------------------------------------------------- class doyle: def find_root(z, t): for i in range(100): v_f = _f(z, t) v_g = _g(z, t) z= z; t= t; r= sqrt(_r(z,t,0,1)) a = ddz_f(z,t) b = ddt_f(z,t) c = ddz_g(z,t) d = ddt_g(z,t) det = a*d-b*c z -= (d*v_f - b*v_g)/det t -= (a*v_g - c*v_f)/det return z,t,r root = find_root(2,0) z = root[0] t = root[1] r = root[2] a = [z * cos(t), z * sin(t)] _z = pow(z, p/q) _t = (p*t+2*pi)/q _r = 0.0 b = [_z * cos(_t), _z * sin(_t)] a= doyle.a; b= doyle.b; r=doyle.r; mod_a = z = doyle.z; t= doyle.t def cmul(w,z): v = [w[0]*z[0] - w[1]*z[1],w[0]*z[1] + w[1]*z[0]] return v def modulus(p): v = sqrt(p[0]*p[0] + p[1]*p[1]) return v def crecip(z): d = pow(z[0],2)+pow(z[1],2) v = [-z[1]/d, z[0]/d] return v circles = [] def Spiral(r, start_point, delta, min_d, max_d): recip_delta = crecip(delta) q = cmul(start_point, recip_delta) mod_q = modulus(q) circle = rg.Circle(rg.Plane.WorldXY, rg.Point3d(q[0], q[1], 0), mod_q*r) circles.Add(circle) q = cmul(q, recip_delta) return circles scale = pow(mod_a, -1) min_d = scale n = n-1 max_d = q*n start = a for i in range(max_d): start = cmul(start, b) Circles = Spiral(r, start, a, min_d, max_d) def mobius(g,c,a,q,bool): G = ghc.trees.Kangaroo2Component.MbiusTransformation(g,c,a,q,bool) return G G = ghc.trees.PolarArray(Circles,rg.Plane.WorldXY,p,2*pi)[0] if T == True: G = ghc.trees.FlipMatrix(G) C = ghc.Circle(rg.Plane.WorldXY,pi*C) G = mobius(G,C,pi/2,Q,False) G = ghc.trees.Rotate(G,pi/2,rg.Plane.WorldZX)[0] G = mobius(G,C,-pi/2,0,False) R = ghc.trees.DeconstructArc(G)[1] P = ghc.trees.Evaluate('if(x>10,0,1)',R) G = ghc.trees.CullPattern(G,P) else: G = ghc.trees.FlipMatrix(G) ``` > **[Doyle spiral](https://en.wikipedia.org/wiki/Doyle_spiral)** > > Pages for logged out editors learn more > > > In the mathematics of circle packing, a Doyle spiral is a pattern of non-crossing circles in the plane in which each circle is surrounded by a ring of six tangent circles. These patterns contain spiral arms formed by circles linked through opposite points of tangency, with their centers on logarithmic spirals of three different shapes. > Doyle spirals are named after mathematician Peter G. Doyle, who made an important contribution to their mathem... ![Doyle_Spiral_V01_2023-01-25_10-13-32](https://us1.discourse-cdn.com/flex022/uploads/dynamobim/original/3X/5/9/59385ea60c9ed21c0b63876f606675ac85c5a5b6.png) ![Doyle_Spiral_V01_2023-01-25_10-13-44](https://us1.discourse-cdn.com/flex022/uploads/dynamobim/original/3X/4/3/43829ac55c60e52aa0b590c54fba6d6590627f2c.png) [Doyle\_Spiral\_V01.dyn](https://forum.dynamobim.com/uploads/short-url/32fNxOyf4ht7zorB4887NZT2sxy.dyn) (96.2 KB)