Koch Fractal Vase

thingiverse

Koch Fractal Vase ============== Model is based on evolving Koch fractal curve. Height of each iteration is adjusted to keep all triangles self-similar, parallel to each other and some of them equilateral. STL model is solid. To print it as a vase use vase mode (option "Spiralize Outer Contour" in Cura). Python code for Blender used to generate models: --- ``` import bpy import math mesh = bpy.data.meshes.new("KochVase") obj = bpy.data.objects.new(mesh.name, mesh) col = bpy.data.collections.get("Collection") col.objects.link(obj) bpy.context.view_layer.objects.active = obj r = 30 # Radius n = 6 # Angle of rotation (phi = pi / n) niter = 10 # Number of iterations phi = math.pi / n ii = 1/(2*math.cos(phi)) dz = r*math.sqrt(3)*math.sqrt(0.75-(math.sin(phi)/math.cos(phi))**2/4) z = 0 verts = [] edges = [] faces = [] for i in range(3): x = r * math.cos(2*math.pi*i/3) y = r * math.sin(2*math.pi*i/3) verts.append((x,y,z)) edges = [[0,1],[1,2],[2,0]] faces = [[0, 2, 1]] def next_vertex(i,j): global phi, ii dx = verts[j][0] - verts[i][0] dy = verts[j][1] - verts[i][1] ndx = math.cos(phi)*dx + math.sin(phi)*dy ndy = -math.sin(phi)*dx + math.cos(phi)*dy return verts[i][0]+ndx*ii, verts[i][1]+ndy*ii lv = [0, 1, 2] le = [[0,1],[1,2],[2,0]] for step in range(niter): z += max(dz,0.4) dz /= math.sqrt(3) ne = [] nv = [] vs = len(lv) for v in lv: nv.append(len(verts)) verts.append(tuple(list(verts[v][:2])+[z])) for e in le[::-1]: v1i = e[0]+vs v2i = e[1]+vs nvi = len(verts) nx, ny = next_vertex(v1i,v2i) nv.append(nvi) verts.append([nx,ny,z]) edges.append([v2i,nvi]) edges.append([nvi,v1i]) if step % 2 == 0: faces.append([e[0],nvi,v1i]) faces.append([e[0],e[1],nvi]) faces.append([e[1],v2i,nvi]) else: faces.append([e[0],nvi,v1i][::-1]) faces.append([e[0],e[1],nvi][::-1]) faces.append([e[1],v2i,nvi][::-1]) ne.append([v2i,nvi]) ne.append([nvi,v1i]) lv = nv le = ne faces.append(list(map(lambda x:x[0],le))) print(le,lv) mesh.from_pydata(verts, edges, faces) ``` ---