Hyper Fractal

The Hyper Fractal is an easy recursive setup for multiple T-Spin Doubles. Recursive in this case means, that after each T-Spin Double the board is in a similar state to setup the next T-Spin Double.

=Introduction=

For every piece there is a preferred spot where you want to place it. The S,Z and O-pieces should be placed on their stacks. the J-pieces are placed in the well atop each other. the L-piece is used to create the T-shaped holes. The I-pieces should be placed in pairs on the O,S or Z-Spots. And finally the T-piece is used for the T-Spin. When everything comes together it could look like this:

=How To Build It=

First steps
Let's look at an example

We initialize the Hyper Fractal main-stack with an I and a Z-piece.

That divides the board in 4 different partitions. On the left we have a 4-wide well that will be filled with J and L pieces to create the T-shaped holes and of course the T-pieces to clear the T-Spins.

The main-stack is divided into 3 partitions: An O-Stack a Z-Stack and an S-Stack.

Now the only thing to worry about is, where to place the I-piece. But luckily that can be solved if we place the I-piece in pairs we can place them on the O,S or Z-stack or we purge them horizontally in the 4-wide well as shown bellow.

But there is one further problem. At the start of the game we have placed to few pieces to start farming T-Spin Doubles and keep the Hyper Fractal going. So we need to build the main-stack first so that we have enough "fuel" for the machine. That means we need to figure where to place the L, J and T-piece on the stack. Luckily there are some ways to do that. L and J-pairs can build rectangles and can be placed on the O-Stack. Or we build a larger rectangle with the L,I and J piece.

The T-piece is a bit tricky because it interacts with the S,Z-stacks. Placing a T-piece on the S-stack transforms it into an Z-Stack and vice versa. That means we need to place the T-pieces in pairs so that after the placement of both T-pieces we have again an intact S and Z-stack. Note that it doesn't matter where we place the two T-pieces. They can stacked up in pairs on either the S or Z-stack or one T-piece each could be placed on both stacks, the end result will always be an S and Z-stack that is accessible, but the stacks might have switched places.

In this example we now stack the J-pieces inside the 4-wide above each other. That means it is recommended to place 2 L-pieces on the main-stack because that way we ensure that we always have an L-piece functioning as an overhang. Together with the other considerations the first 14 pieces could be placed like this:

Note that these are not really the first 14 pieces because in the example we already placed an I-piece and Z-piece first but the main idea remains the same. To summarize: It is recommended to place 1 or 2 pairs of T-pieces and more L-pieces than J pieces on the main-stack before starting the Hyper Fractal loop.

Starting The Loop
So let's look at the main trick of the Hyper Fractal. Spinning the L-pieces between the J-piece stack. It is better to spin the L-piece in a position so that it looks like an actual "L" when placing it in the stack and rotating it when it comes in contact with the first block or the floor. Placing the L-piece "upside-down" could lead to it getting stuck and not able to rotate anymore.

If the main stack is high enough, at least 3 or 4 J-pieces are placed and 2 L pieces are already rotated in the J-stack to create 2 T-shaped holes it is time to start the loop. Now you spin every L-piece in to create another T-shaped hole and every T-piece to clear the T-Spin. Make sure to keep the main stack relatively flat while building. So when possible the pair of I-pieces should always be placed on the lowest partition of the main stack.

But keep in mind, that it would be preferable to hard drop the L-piece in order to maximize speed. Don't forget to place the J after it or else there is no T-Spin and trying to clear with a T-piece only results in a double line-clear.

Main Stack Management
Knowing how to build the main stack in different ways is very helpful, because the Hyper Fractal is burning the "fuel" of the main stack. With each loop we clear 30 blocks (L-Spin line clear + T-Spin). But all 7 pieces together add only up to 28 blocks. So the main stack runs out of fuel 2 blocks per loop. That means we need to use some of the J, L, T-pieces on the main stack after a while. In order to do that it is also important to know how to stack the other 4 pieces so that the main stack doesn't become too uneven.

Let's look at the S,Z-stacks that can occur in 2 different configurations:

Here are some further stacking options for these cases.

The O,S,Z-pieces can transform the open configuration into the closed configuration:

The same result can be achieved with either two S or Z-pieces.

The closed configuration can be preserved in this way:

The closed configuration can be transformed into the open configuration in this way:

=Alternative Setups=

Similar to the example we used at the beginning there are other ways to create simple setups for the Hyper Fractal.

Keep in mind that every setup can also be mirrored. But not only that. Because the 4 partitions can be stacked independently and don't need to interact with each other, every permutation yields also a valid setup. Furthermore there are always two main methods to fill the well by either stacking the J or the L-pieces.

These considerations lead us to the realization that there are at least 48 alternative setups, including the original example. By understanding the modular nature of the different stacking-setups it is easier to see how to transition into a Hyper Fractal in a variety of situations.

Here are a few examples how the O,S,Z-stacks could also be placed:

The T-Opening
One other way to setup the Hyper Fractal is by placing a single T-piece that functions as the base for the S,Z-stack.

One drawback for this setup is that it breaks the symmetry of the S,Z-stack and therefore rules out some easily accessible stacking options. But other options become available. In fact, it is possible to transform the 6-wide main-stack from a stack with a broken symmetry S,Z-stack in a symmetrical S,Z-stack and vice versa. The key is placing another T-piece. Here are a few examples:

7 Piece Opening
For an Opening it is important to know how to use all 7 pieces of the first bag. An Opening of the Hyper Fractal should focus on building the main stack first.

It has a broken symmetry S,Z-stack but that can be fixed. For example like this:

=Helpful Advice=

J,S,Z-Skimming
One useful technique for balancing the stack is J-skimming (L-skimming in the mirrored setup) if the J-stack is to high. By rotating a J-piece instead of an L-piece, it creates a shape that can be cleared with either an S or a Z-piece. That operation just clears a J-piece from the stack so the board will be in the standard state again. It is also possible to place the S or Z-piece first and skim with J or L-piece later.