Fractal Matrix Architecture – Studio Jack Rendler

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Fractal Matrix Architecture

In the field of mathematics, a matrix is: “ a rectangular array of quantities or expressions in rows and columns that is treated as a single entity and manipulated according to particular rules .” This workshop will explore orthogonal, cubic, and rectangular geometrical systems using algorithmic software. We will delve into the fragmentation and deconstruction of volumes, surfaces, and line-work to create systems of grids and subdivisions. We will be working with recursivity, which involves the continuous multiplication and sub-division of geometry that leads to the creation of complex schematics. Such workflows may be helpful in engaging with urban contexts or tectonic particularities.

The software used in the course will be Rhino and Grasshopper with the plug-in Pufferfish and an introduction to Mandelbulb 3D.

The Scope of the Workshop:

The workshop will primarily focus on Grasshopper and the plug-in Pufferfish to explore geometrical operations. We will look at techniques that yield certain results as we work with specific geometric typologies. The geometric typologies that will be examined will be orthogonal, cubic, and rectangular geometrical systems. We will examine particular geometry operations, the grouping of geometric clusters, their scaling and dispersion, and the subdivision and isolation of specific components. We will also be exploring the formation of fractals in the Mandelbulb 3D software. In Mandelbulb 3D, we will introduce the interface and basic formulas inside the software. We will also guide you through exporting your Mandelbulb 3D mesh into Rhino.


The workshop will focus on orthogonal geometries as geometric systems, like shifting grids and subdivided volumes.
Through hands-on exercises, We will guide you in the process of subdividing regions and rectangles using Pufferfish grasshopper components and the substrate component of grasshopper.

  • We will be offsetting surfaces at variant distances and extruding at variant lengths, creating arrays and fields of geometric compositions
  • We will explore different ways of integrating fields of line works and surfaces to create aggregations of clusters and volumes.

    As a relative but separate note, we will provide an introduction to Mandelbulb 3D, where fractal structures will be explored.
  • How to navigate the Mandelbulb 3D interface.
  • Introduction to particular formulas.
  • Formula parameter modification techniques.
  • Exporting voxel stacks from Mandelbulb 3D using the Fiji J Image Compiler.


  • Comprehend the manipulation of complex geometrical systems by operating on the parameters that drive the system.
  • More fluidly compose the aggregation of shifting grids and subdivided volumes as integrated schematics.
  • Understand the nature of Fractals in a more intimate sense and how they function and form.


Day 1:

  • Contextual Lecture – Regarding Jack’s book (Terrestrial Architecture)
  • What are the applications of prototypical abstract geometries as fractal matrices?
  • Grasshopper operation methodology with the Pufferfish plug-in
  • Project Assignments
  • Q&A

Day 2:

  • Grasshopper Script Elaborations
  • Introduction to Mandelbulb 3D
  • Project Development and Reviews
  • Q&A


  • Rhino (Download)
  • Grasshopper
  • Pufferfish Plug-in for grasshopper (Required) (Download)
  • V – Ray (Optional)
  • Mandelbulb 3D (Required) (Download)
  • Fiji ImageJ Image compiler (Required) (Download)


Jack Rendler

Jack Oliva-Rendler is exploring work processes in Digital 3D modeling, Geospatial Information. Systems (GIS) and algorithmic modeling methods for multi-scaler ecological solutions, planetary, bio-regional, infrastructural, local, and community-based scales of work. Jack attended the internationally renowned “Southern California Institute of Architecture” where he developed skills in metaphysical and computational philosophy and design technology to win an Undergraduate Thesis Prize – he also received a master’s Degree in Architecture from Harvard Graduate School of Design – during his graduate studies, he received an award from Mars City Design, in the Urban Design Category in the Mars City Design Competition, with panelists and judges from NASA and Dassault Systems.

Jack’s thesis projects at both institutions proposed radical data infrastructures for Earth Observation Science and environmental analysis. Jack’s design specialties have evolved to include fractal formulations and mathematical simulations in Mandelbulb 3D and Grasshopper to simulate organic and crystallographic fractal systems with many applications. His book Terrestrial Architecture is out now.

Important Notes:

  • The “Fractal Matrix Architecture ” Studio workshop by PAACADEMY will start on Saturday, 15th June 2024, at 14:00 (GMT).
  • Total sessions: 2 Sessions
  • The teaching duration per session will be 4 hours.
  • Students will have time for a break between teaching hours.
  • Each session and the entire studio will be recorded, and videos will be available for participants just a day after the class for unlimited time.
  • PAACADEMY will provide a certificate of attendance.
  • The studio has limited seats. Tickets are non-transferable & non-refundable. Please read carefully before you register.
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