Maybe it’s because it’s nearly summer. Maybe it’s because I finally finished my finals. Maybe it’s all a result of coincidence and random web browsing. Whatever the reason, I feel like filling my blog with warm, happy colors this weekend. What better place to begin, than with a fractal?
A Fractal Sunset
(look below to see it "set")
This is a combination of sets, each transformed to simulate ripples on a lake. One (the mountain range) is a Julia set, while the other (the sun) is the modified interior of a Mandelbrot set. Usually, when you see a Mandelbrot set or Julia set you see busy spirals or complex curves. But zoom in to the right area, or start with the right seed, and the curves can be calming rather than complex. I tried to capture a bit of the soft variation that arises in such a set by creating an animation. The animation is a result of slowly adjusting one of the coloring variables in the Mandelbrot set.
It looks quite a bit like something I haven’t had time to watch lately... the sun setting behind the foothills, reflected on a nearby lake:
Luckily, I’m now on summer break. That means I have time to do the things I enjoy, like watch sunsets, create fractals, and blog. So, on that note, stay tuned for more red, orange, and yellow fun!
My name is Jason D. Padgett. I'm a math/quantum physics student in Washington state. I have found where fractals arise from. I can show you how to hand draw a fractal of literally anything. Since you're into fractals you will love this.
Please email me at firstname.lastname@example.org and I will email you the diagrams. If you would like to see my explanation, go to fantastic fractals and click on the button that says "how to make a fractal". It shows how to make a fractal of anything.
By the way, your pictures are beautiful. I love all water fractals because they move like energy (all waves). Please email me, you will not be disappointed for I'm not exaggerating at all.
Jason, I apologize for the slow response. I need to catch up with my e-mail box, still, so don't worry, I had planned to write you, I just haven't had the time yet. (That goes for a few other people out there too... I promise I'll catch up soon!)
I read your explanation and quite enjoyed it. I used to make all sorts of patterns with a straightedge and compass, but never quite did anything like that. It's pretty cool. I'll try to comment more when I e-mail you, and perhaps someday base a Friday fractal around the idea. In the meantime, I hope some other fractal fans who read here might check it out as well. Thanks for writing!
Thanks for checking out the 'How to make a fractal' at fantastic fractals. I just posted several other drawings at fine art america (just type my name under 'find artist') and it will take you to my page. I've got 8 or nine different drawings there. I'm going to post more, but right now I'm in Pskov Russia until July 12 2008 and I can't accessw my files from here. If you get a chance check them out. If you draw one yourself you can change the way they look by slicing the shapes into different angles. I use right triangles because that is how energy flows but you can use different types of triangles or even other polygons to change the shapes that evolve in the center of the fractals. Or you can add depth by making the shapes larger and smaller as you 'fractal' the diagram. Hopefully I'll have one of these drawn soon and at the same web page so others can learn the method and hopefully make new discoveries. Have a great day.