I like Western-Islamic World View Conflicts as a starting point (HT to T). The applicable project, The Struggle of Narratives-Attempting to Visualize It (11 pdfs):

Project Description

Background

However else we characterize the current world situation, we must acknowledge that we are involved in a struggle of worldviews (or as some have called it, a "struggle of narratives"). It may not be a Huntington's "clash of civilizations" but it is most certainly a struggle of ideas. Among the topics we considered in this project are:

What do we mean by struggle of narratives as a context within which diplomacy, politics and the use of force takes place?

How is this more than simply the old battle for the "hearts and minds" of the populace?

Can the pitched battle of the media be thought of as the "New Fog of War" quite different from that described by Clausewitz?

How might a picture of this struggle look from the point of view of our visualization of public policy?

Are there new ways to portray the ideological conflict that might help us understand this process more deeply?
...
Wicked problems

Our view is complex public policy issues constitute what Horst Rittel has called "wicked problems." We sometimes call them ill-structured problems and more informally "social messes."

Wicked problems are situations that have these properties:

complicated, complex, and ambiguous

uncertainty even as to what the problems are, let alone what the solutions might be

great constraints

tightly interconnected, economically, socially, politically, technologically

seen differently from different points of view, and quite different worldviews

contain many value conflicts

are often a-logical or illogical
... (much more)
JMM Comments on the Western-Islamic World View Conflicts chart.

I'd suggest that someone more qualified than myself check out the bullet points for the Traditional Islamic View and for the Militant Islamic Beliefs (the latter appear to be based on Maududi). Whoever does that should be a firm Muslim Traditionalist. I'd also suggest that the Islamic World is not so simple; e.g., the basic division between Sunni and Shia.

Western Constitutional / Democratic / Capitalistic Ideology is scarcely a monolith with huge differences in Worldview between various blocks. I'm drawing out in my head at least a half-dozen blocks - and they are not all "Western". So, the Western Constitutional / Democratic / Capitalistic Ideology as stated is an idealized set of bullet points.

Taking the "Western Constitutional / Democratic / Capitalistic Ideology" as a given, solely for purposes of discussion, one should add a "Western" Left Hook (POW !, as the cartoons say) entitled "Western Attack". That to match the Islamic Left Hook entitled "Militant Counterattack" (POW !). Of course, that immediately leads to an argument as to who attacked first - ah, yes, competing narratives.

The parent webpage, R. Horn Home, leads to his Bio:

Robert E. Horn is a political scientist with a special interest in policy communication, social learning, and knowledge management (especially in biotechnology and national security affairs). For the past 7 years, he has been a visiting scholar at Stanford University's Center for the Study of Language and Information. His career has been widely interdisciplinary, leading a team (in the 1960s) that developed an information system covering 400 federal programs on education and training, editing a standard reference work that evaluated over 1,500 educational simulations in 35 academic disciplines (in the 1970s), and creating, while he was a research associate at Columbia University, a widely used methodology for the analysis of any complex subject matter. He turned this research into an international consulting company, specializing in knowledge management, called Information Mapping, Inc., (in the 1980s) which he founded and was CEO of for 15 years. He has taught at Harvard, Columbia, and Sheffield (U.K.) universities

His recent development of visual argumentation mapping has resulted in the publication of the Mapping Great Debates series, which, in the past year and a half, has received a full-page review in Nature, as well as being hung in a national museum in The Hague as part of an exhibit on information design as a fine art.

Horn is also Vice President of the Meridian International Institute on Governance, Leadership Learning and the Future, which is a policy think tank. For the past several years, he has been leading a project exploring the possibilities for using highly visual cognitive maps to aid the policy making process (especially science and security matters). His most recently published book is Visual Language: Global Communication for the 21st Century (www.macrovu.com). At Stanford he continues his research work in knowledge management and information design. His consulting clients have included Boeing, Lucent Technologies, Principal Financial, AT&T, HP, and other Global 1000 companies.

This year he was awarded a Lifetime Achievement Award for the work on the Information Mapping method from the Association of Computing Machinery (ACM). He is a fellow of the World Academy of Art and Science and a member of its nominations committee. He is a Woodrow Wilson Fellow and a recipient of the Outstanding Research Award from the National Society for Performance and Instruction (NSPI).
Lots of "stuff" - too much "stuff" ? (you judge).

Regards

Mike