http://people.csail.mit.edu/jaffer/Marbling/Pattern-Welding

# Pattern Welding

Bladesmiths John D. Smith and Zack Jonas had a booth at the 2011 Lowell Folk Festival where they showed their beautiful pattern-welded steel knives. Inquiring about their techniques, I realized that what they do is 3-dimensional marbling!

First, they forge a bar of alternating steel (longways) layers having two different compositions (and appearance).

There are several techniques which can be combined to create a variety of patterns. A simple one is to twist a (heated) bar tightly, so that it looks like a cable. The blade is then created by slicing it out of the twisted bar.

The transform to twist a bar along its axis (p3) without changing its length is:

 T(p, c) = p ⋅ [ cos c⋅p3−sin c⋅p30 sin c⋅p3cos c⋅p30 0 0 1 ]

Vector p = [p1, p2, p3]. Large c values twist tightly. The inverse transform T −1(p,c)=T(p,−c). T(p,c)−p is not a vector field because its magnitude becomes unbounded with distance from the axis of rotation. However, for finite volumes, T is volume-preserving; the transform simply rotates each p1×p2 plane by an amount proportional to its p3 coordinate.

Below are slices through simulated pattern-welded bars with 0, 1/2, 1, 2, and 4 full twists. The left two columns are sliced midway between the center and minimum radius. The right column is sliced through the center.

13 layers 12 layers 12 layers, sliced through center
PostScript code PostScript code PostScript code