Patterns for a strip of leds
It can be done without microcontroller, but as it often happens it will be easier if you use a microcontroller.  

You'll need a series of SIPO (Serial-In, Parallel-Out) shift registers, like the 74HC164, where you connect the last output bit of one shift register to the input of the next. Then on each clock pulse your pattern will shift one position through the chain. If you connect the last bit of the last shift register back to the input of the first you get a loop through which the pattern will shift forever.  

The thing is to get the pattern in, in the first place. Most shift registers have a CLEAR input which makes all outputs low, but we also have to initialize some outputs high, or there will be very little to see. That can be done by inserting a couple of 74HC195s. They're the same as the 74HC164, but only 4-bit because they need some pins for parallel-load data. Setting these high allows you to insert a series of 1s in an otherwise 0 chain.  

Use an RC reset circuit to preset the chain at startup, and use a low frequency oscillator to clock.  

We still haven't used our microcontroller, so where does this come in? The microcontroller allows you to create much more complex patterns, actually 2\$^{60}\$ or 1 152 921 504 606 846 976 of them. It can replace the oscillator and reset circuit, and you won't need the 74HC195s. And you can keep it small, since we only need two I/Os: serial data and clock. (Reset isn't required if we shift the pattern in quickly at initialization.) So, let's see, which microcontroller is suitable for this? How about the PIC10F200!? :-) 

There we go again(!): small 6-pin package, internal oscillator, enough memory to store a 60 bit pattern, no external components required, expect for 8 74HC164 shift registers.