A turtleocracy is an organizational and decision-making structure. It's an alternative to democracy, do-ocracy, bureaucracy, consultancy, etc. See comparisons with these other forms at Is Turtleocracy Right for Your Organization?
(Cross-Org Turtleocracies? A turtleocracy can span more than one organization.)
There are three big ideas.
🌪 The Turtle Cycle. Each turtle will go through cycles or phases that include consultation with experts in related fields, individual reflection on their question, and experimentation. They should be adequately resourced and encouraged in such cycles, and Turtleocracy and Turtle Check meetings are there to make sure they are so resourced. 
🕸 Web of Questions. The organization structure is based on a network of deep questions. Each question has a turtle-y person attached. These turtles dedicate themselves to researching their question over a fairly long term. One turtle can have more than one question, and one question can be in more than one place in the network. Each turtle has certain working relationships with turtles they are connected to in the network, but they are not the traditional relationships of bosses and employees: turtles cannot tell other turtles what to do.
<aside> 🌲 Example Web. One question might be something like "how can we reorganize technology to support human flourishing?" And connected to that may be questions like "what is human flourishing" and "what are the different ways of organizing technology" and other questions, about theories of change, influence, messaging, and so on. Each question has a person pursuing it, so both the questions and people are arranged in a network.
For a complete example, check out the HS Web of Questions for Human Systems.
A turtle gathers information from multiple problem-solution fields that already exist. They run experiments based on guesses about what might work for their own project, and reflect on the outcomes without being committed to any particular approach. Turtles are always tentative in their answers, and guided by what works. They are prepared to repeat the process of research, experimentation, and reflection for years.
If you want to do research inside a turtleocracy, you will go through certain stages. See ‣ to see our intake process. Once you are inside, you'll go through the turtle cycle.
Turtles flow between states or phases, with occasional Turtle Check meetings to ensure they are adequately resourced and the questions are all still aligned.
<aside> ☝ It may also be a good idea to replay Turtles Rule Game as a group periodically to see if there are new questions, or if the questions have changed.
Turtleocracy is designed to address problems with other org structures. In other orgs, important information—about people's personal values, and their doubts about the organizations' work—tends to get lost. We believe that these two types of information are especially important for the economy we want to create: one that's (a) focused on meaning and values over business goals, and (b) that takes more doubts and larger-scope issues into consideration as the organization operates. (See Towards “Game B” for more on the economy we want to create, and why this has something to do with values and doubts.)
Here are examples of the kinds of problems Turtleocracy is designed to address: