![]() The same thing seems to happen with the line thickness too - I wanted all the designs to be at 0.1, but it kept changing it back to 1.0. Grapher does allow you to increase the resolution, but it’s not sticky - change anything in the equation and it pops right back to the default. If the line is going from one side of the graph to the other and back again a thousand times in a couple of radians, you don’t want the graph program to start dropping line segments, or corners, or anything really. I’m sure for most graphs the default resolution is fine, but when creating these patterns you need tiny increments. First of these is the resolution of drawing the graph. There are still some extremely frustrating limitations though. I give Grapher another go, and at last, I can create and export patterns: Again, not much - not much that I could afford, that is. ![]() I got a couple of patterns out of it and had a look round for other options. It could create the patterns, most of the time, and export to EPS, though not always. Aha! Now here was a program that could create the patterns I was after and export to EPS. Then, a couple of years later I discovered Grapher on the Mac. The process took ages and served just to prove to me that I could do it, but the results were too poor to go much further. So off I went, using the hypotrochoid equations on Mathworld to create rather rough and ready patterns - scripting at this point didn’t have a very usable set of functions for creating beziers, so I had to use crummy line segments. I do, however, have a computer, and at the point I first started playing with the designs (mid-2004) Illustrator and Photoshop had gained the ability to be scripted. The mathematical process attracted me immediately as I don’t have a geometric lathe and nor do I have anywhere to put one. ![]() Central to banknote designs are Guilloche patterns, which can be created mechanically with a geometric lathe, or more likely these days, mathematically. I can get lost for hours in all the details, seeing how the patterns fit together, how the lettering works, the tiny security ‘flaws’ - they’re amazing. ![]()
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