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You want a group's symbolism and ideology to mesh together. That's not hard at all. Start with the group's core idea. What is it that they are, most of all? If you could sum up their "ideology" in...
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Source: https://writers.stackexchange.com/a/42239 License name: CC BY-SA 3.0 License URL: https://creativecommons.org/licenses/by-sa/3.0/
#3: Attribution notice added
Source: https://writers.stackexchange.com/a/42239 License name: CC BY-SA 3.0 License URL: https://creativecommons.org/licenses/by-sa/3.0/
#2: Initial revision
You want a group's symbolism and ideology to mesh together. That's not hard at all. Start with the group's core idea. What is it that they are, most of all? If you could sum up their "ideology" in one word or phrase, what would it be? (Examples could be: honour, wisdom, survival, paying your debts, etc.) Next step: write that core word/phrase on a page, and start throwing associations around it. Look in particular for natural motifs (animals, plants, landscape features), but consider also other phrases that come to mind, citations, people, historic events, etc. Colours or colour combinations could also arise from this associations chart. Consider, for example red and gold - Richard the Lionheart's crest, thus courage. Red, white and blue would lead to the French cokcarde, thus to liberty. And so on. If you find something is still lacking, consider what secondary themes you want associated with your faction, and throw associations around those. In the end, pull everything together - philosophy, crest, motto, et voila, you're all set.