Stewart Dickson
60 Claremont Court
Champaign, IL  61822 USA
+1(217)607-1024

mathart(a)emsh.calarts.edu

Portfolio of 3D Fractals

Artist's Statement

3D Julia Set, computer-rendered volume visualization, (c) 1993 Stewart Dickson courtesy of The Williams Gallery.

An view down the positive Z-axis of a 200 x 200 x 200 x 8-bit per pixel volume convergence map of the procedure Z -> Z^2 + (-0.1103,-0.67037,0.0,0.0) where Z is a complex quaternion four-vector of the form (a, b i, c j, d k). The pixel volume represents the three-space spanned by (1, i, j, 0). This image is part of a proposed collaboration to construct a physical model of this object via Selective Laser Sintering technology at the Department of Mechanical Engineering, University of Texas at Austin. Contact: richc@mcl.cc.utexas.edu

Software/Hardware used: Quaternion Julia Set calculator by Stewart Dickson interfaced to the Army High-Performance Computing Research Center (AHPCRC), University of Minnesota, "Brick of Bytes" (BOB) public-domain volume visualization software on a Silicon Graphics Personal Iris 4D/35TG graphical workstation.

3D Julia Set, computer-rendered volume visualization, (c) 1993 Stewart Dickson courtesy of the Williams Gallery.

Cross-sections parallel to the X-Y plane at Z = 0.0, 0.5 and 1.0 of a 2048 x 1536 x 1 x 8 bit per pixel volume convergence map of the procedure Z -> Z^2 + (-0.1103,-0.67037,0.0,0.0)

Software/Hardware used: Quaternion Julia Set calculator by Stewart Dickson on a Silicon Graphics Personal Iris 4D/35TG graphical workstation.

3D Julia Set, computer-rendered volume visualization, (c) 1993 Stewart Dickson courtesy of the Williams Gallery.

Cross-sections parallel to the X-Z plane at Y = 0.0 and 0.5 of a 200 x 200 x 200 x 8 bit per pixel volume convergence map of the procedure Z -> Z^2 + (-0.1103,-0.67037,0.0,0.0).

Software/Hardware used: Quaternion Julia Set calculator by Stewart Dickson interfaced to the Army High-Performance Computing Research Center (AHPCRC), University of Minnesota, "Brick of Bytes" (BOB) public-domain volume visualization software on a Silicon Graphics Personal Iris 4D/35TG graphical workstation.

3D Julia Set, computer-rendered volume visualization, (c) 1993 Stewart Dickson courtesy of the Williams Gallery.

An oblique view from approximately (-1, 1, 0) of a 200 x 200 x 200 x 8 bit per pixel volume convergence map of the procedure Z -> Z^2 + (-0.1103,-0.67037,0.0,0.0).

Software/Hardware used: Quaternion Julia Set calculator by Stewart Dickson interfaced to the Army High-Performance Computing Research Center (AHPCRC), University of Minnesota, "Brick of Bytes" (BOB) public-domain volume visualization software on a Silicon Graphics Personal Iris 4D/35TG graphical workstation.

3D Julia Set, computer-rendered volume visualization, (c) 1993 Stewart Dickson courtesy of the Williams Gallery.

Cross sections parallel to the Y-Z plane at X = 0.0 and 0.5 of a 200 x 200 x 200 x 8 bit per pixel volume convergence map of the procedure Z -> Z^2 + (-0.1103,-0.67037,0.0,0.0).

Software/Hardware used: Quaternion Julia Set calculator by Stewart Dickson interfaced to the Army High-Performance Computing Research Center (AHPCRC), University of Minnesota, "Brick of Bytes" (BOB) public-domain volume visualization software on a Silicon Graphics Personal Iris 4D/35TG graphical workstation.

Convergence map of the procedureZ -> Z^2 + (0.04133,0.62491,0.05,0.05) rotating in complex four-space. (1.1Mbyte AVI)

Convergence map of the procedureZ -> Z^2 + (0.04133,0.62491,0.05,0.05) rotating in complex four-space. (1.1Mbyte AVI)

3D Julia Set, computer-rendered volume visualization, (c) 1993 Stewart Dickson courtesy of the Williams Gallery.

An oblique view of a 200 x 200 x 200 x 8 bit per pixel volume convergence map of the procedure Z -> e^(i pi/2) Z^2 + e^(-i pi/2) (0.2809,-0.53,0.0,0.0) in which the Julia set is rotated 90 degrees in the complex plane. Z is a complex quaternion four-vector of the form (a, b i, c j, d k). The pixel volume represents the three-space spanned by (1, i, j, 0).

This image is part of a proposed collaboration to construct a physical model of this object via Selective Laser Sintering technology at the Department of Mechanical Engineering, University of Texas at Austin.

Software/Hardware used: Quaternion Julia Set calculator by Stewart Dickson interfaced to the Army High-Performance Computing Research Center (AHPCRC), University of Minnesota, "Brick of Bytes" (BOB) public-domain volume visualization software on a Silicon Graphics Personal Iris 4D/35TG graphical workstation.

3D Julia Set, Selective laser-sintered computer-rendered volume visualization, Dimensions: 2" X 4" X 1"; (c) 1993 Stewart Dickson courtesy of the Williams Gallery.

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The physical 3D construction of a 200 x 200 x 200 x 1 bit per pixel volume convergence map of the procedure Z -> e^(i pi/2) Z^2 + e^(-i pi/2) (0.2809,-0.53,0.0,0.0) in which the Julia set is rotated 90 degrees in the complex plane. Z is a complex quaternion four-vector of the form (a, b i, c j, d k). The pixel volume represents the three-space spanned by (1, i, j, 0).

Software/Hardware used: Quaternion Julia Set calculator, data format conversion software by Stewart Dickson, Selective Laser Sintering by the Department of Mechanical Engineering, University of Texas at Austin.

3D Julia Set, 4 sequential views, rotated about the Z-axis, of a computer-rendered volume visualization, (c) 1993 Stewart Dickson courtesy of the Williams Gallery.

Renderings of a 512 x 512 x 512 x 8 pixel volume convergence map of the procedure Z -> (e^(i pi/2)) Z^2 + (e^(-i pi/2)) (-0.745,0.113,0.01,0.01). This image is part of a proposed collaboration to construct a physical model of this object via Selective Laser Sintering technology at the Department of Mechanical Engineering, University of Texas at Austin.

Software/Hardware used: Quaternion Julia Set calculator by Stewart Dickson. This database was calculated in approximately 13 hours on the SGI 4D/35 (35MHz MIPS R3000 RISC CPU). The rendering was made using ChapVolumes on a Pixar Image Computer.

512x512x512 Julia set C = (-0.745,0.113,0.01,0.01) rotating in complex 4-space. (1.5Mbyte Quicktime) (596Kbyte AVI)

Proposal for the 3D Zoetrope of the 512x512x512 Julia set C = (-0.745,0.113,0.01,0.01) rotating in complex 4-space. (296Kbyte Quicktime) (436Kbyte AVI)

Software/Hardware used:Quaternion Julia Set calculator by Stewart Dickson; Kitware's Visualization ToolKit Apple dual-2.7GHz G5 PowerMac.

See also: A Proposal to Replicate the Fractal Zoom in Three Physical Dimensions

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