# Mathematical Surface

In this grasshopper example file, by remapping the mesh vertices and computing the sine of its values, we can define a mathematical surface.

In this grasshopper example file, by remapping the mesh vertices and computing the sine of its values, we can define a mathematical surface.

In this grasshopper example file by defining a closed polyline and using the Kangaroo plugin you can create a parametric minimal surface.

In this grasshopper definition, you can model a Schwartz minimal surface by using the Jellyfish plugin.

In this grasshopper definition you can create a space filling fractal by generating grid of rectangles and applying a growth system to it.

In this grasshopper definition by creating series of circles and creating panels from each of them you can create a polar plaid pattern.

In this grasshopper definition, you can model a series of triangular extrusions by defining a simple polygon. Anemone plugin has been used for the recursive loop.

In this grasshopper definition, you can create a series of different forms and geometries by changing the domain of a trimmed Enneper surface.

In this grasshopper definition, you can model a Klein bottle using Parakeet’s plugin. Then you can twist the mesh around an axis and finally create a contour from the mesh and extract the curves.

In this Grasshopper definition, you can model a parametric Enneper surface by using the Lunchbox Plugin and extracting the Iso-curves.

In this grasshopper definition by using the Parakeet’s pattern genotype inside an hexagon, you can model a parametric pattern model.

In this grasshopper definition you can model a wavy like frame structure around a sphere. First we will extract the vertices of the sphere and then use a Sine*Cosine function to move them around.

In this grasshopper definition you can learn how to use the Millipede’s geometry wrapper to model a mesh around a curve and control it with different parameters.

In this grasshopper definition first we model an Icosahedron by Weaverbird and then generate wave pattern on it by using Mesh+ Plugin. Finally you can also make the mesh thicker and smoother.

In this grasshopper definition by defining a base pattern you can generate a kaleidoscope by using the Parakeet plugin.

In this grasshopper definition, you can create noise on any surface by using the Tundra plugin. For example we have used the Mobius surface component by Lunchbox plugin.

In this grasshopper definition, by using the Fox & Pufferfish plugin you can model different expressions of minimal surfaces.

In this grasshopper definition, you can create a voxelized shell shape by subtracting two volumes and finally model a Triply Periodic Minimal Surface.

In this grasshopper definition you can create a 3d sine iso surface by using the Axolotl Plugin.

In this grasshopper definition by using standard minimal surface equations, you can create different minimal surfaces and also use Align vertices to avoid generating an invalid mesh.

In this grasshopper definition by using the PerlinNoise component of the Noise 4d plugin you can produce a changing value for a iso surface which is generated with Millipede.You can also subdivide the mesh surface to have a smoother result.

In this grasshopper definition you can create a surface which is based on the Chladni equation. You can also make the mesh faces colorful by a gradient and Subdivide the surface by Weaverbird plugin to have a smoother mesh.

In this grasshopper definition you can create a grid of boxes and change their oreintations by using the CurlNoise Component.

In this grasshopper definition you can use the “facet dome” component to cover a sphere with voronoi cells and then move the centroid in the normal direction to finish the model.Finally you can use the weaverbird plugin to smooth the geometry.

In this grasshopper definition by exploding a mesh sphere and by using the Pufferfish plugin you can extrude the faces towards their normals controlled by a sine wave.

In this definition you can model a fractal based on a square which builds two smaller squares on one of its edges.

In this definition you can make a fractal rotating polygon by using the Anemone plugin. First we are going to explode the curve to its segments and then evaluate a point on the edges. This recursive algorithm will produce the final rotating polygons.

In this grasshopper definition you can model the shadow of a hypercube(tesseract). In geometry, a hypercube is an n-dimensional analogue of a square and a cube.

In this grasshopper definition you can model a parametric 3d curve by giving a base curve.

In this grasshopper definition by using the 3d Maurer rose formula and combining it with Dendro plugin you can create a parametric form. In geometry, the concept of a Maurer rose was introduced by Peter M. Maurer.

In this grasshopper definition by creating relative tangent spheres which revolve around each other you can create different spirograph patterns in 3d space you can also use Dendro plugin to convert these complex curve to volume.