This article presents fractal design concepts for stretchable electronics, demonstrating how fractal geometries can be used to create advanced electronic devices with enhanced mechanical and electrical properties. The study shows that thin films of hard electronic materials, patterned in deterministic fractal motifs and bonded to elastomers, enable unusual mechanics with important implications in stretchable device design. Fractal-based structures, such as Peano, Greek cross, and Vicsek curves, are used to create space-filling structures of electronic materials, including monocrystalline silicon, for applications such as electrophysiological sensors, precision monitors, actuators, and radio frequency antennas. These devices support conformal mounting on the skin and have unique properties such as invisibility under magnetic resonance imaging. The field of stretchable electronics is of growing interest, motivated by fundamental considerations in material science and application spaces in areas such as biomedicine. A core challenge is in achieving high-performance electronic functionality with systems that offer elastic, low modulus responses to large strain deformations. Two of the most successful approaches to this problem exploit advanced composites. The first involves dispersing conducting or semiconducting nanomaterials into elastomeric matrices. The second exploits alternative classes of composites, created deterministically by using thin layers of electronic materials lithographically defined into two-dimensional filamentary mesh layouts. The study shows that concepts in fractal geometry, which are known to determine behaviors in traditional 3D networks and are pervasive in biological systems, can be successfully exploited in 2D deterministic systems, with important functional consequences in advanced stretchable electronics. Fractal-based structures can be described by self-similarity: subdivision into small sections yields pieces with geometries that resemble the whole. Compared with previously explored networks of periodic serpentine shapes, fractal designs can be engineered to accommodate enhanced elastic strain along a selected dimension and to support biaxial, radial and other deformation modes. In addition, the choices of topologies span a rich range, from lines to loops, capable of tailoring to specific electronic applications through integration and interdigitation of multiple structures. The results illustrate the diversity of possibilities through both the finite element method (FEM) and experimental demonstration. The approximate fractal dimensions in these finite-iterative curves range from 1.5 to 2. The elastic tensile strains achieved with these structures indicate that they are suitable for use in various stretchable devices, including the epidermal electronic platform, with key advantages over previously described layouts. The study also demonstrates the mechanics and electronics of Peano-based geometries, showing that the Peano curve provides a model system for examining the detailed mechanics of fractal-based motifs. The results indicate that Peano layouts with unit cells all oriented in the same way maximize the uniaxial stretchability along the unit cell direction. The 'half-and-half' Peano layout, which contains unit cells with alternating orientations, balances the maximum strain supported along the xThis article presents fractal design concepts for stretchable electronics, demonstrating how fractal geometries can be used to create advanced electronic devices with enhanced mechanical and electrical properties. The study shows that thin films of hard electronic materials, patterned in deterministic fractal motifs and bonded to elastomers, enable unusual mechanics with important implications in stretchable device design. Fractal-based structures, such as Peano, Greek cross, and Vicsek curves, are used to create space-filling structures of electronic materials, including monocrystalline silicon, for applications such as electrophysiological sensors, precision monitors, actuators, and radio frequency antennas. These devices support conformal mounting on the skin and have unique properties such as invisibility under magnetic resonance imaging. The field of stretchable electronics is of growing interest, motivated by fundamental considerations in material science and application spaces in areas such as biomedicine. A core challenge is in achieving high-performance electronic functionality with systems that offer elastic, low modulus responses to large strain deformations. Two of the most successful approaches to this problem exploit advanced composites. The first involves dispersing conducting or semiconducting nanomaterials into elastomeric matrices. The second exploits alternative classes of composites, created deterministically by using thin layers of electronic materials lithographically defined into two-dimensional filamentary mesh layouts. The study shows that concepts in fractal geometry, which are known to determine behaviors in traditional 3D networks and are pervasive in biological systems, can be successfully exploited in 2D deterministic systems, with important functional consequences in advanced stretchable electronics. Fractal-based structures can be described by self-similarity: subdivision into small sections yields pieces with geometries that resemble the whole. Compared with previously explored networks of periodic serpentine shapes, fractal designs can be engineered to accommodate enhanced elastic strain along a selected dimension and to support biaxial, radial and other deformation modes. In addition, the choices of topologies span a rich range, from lines to loops, capable of tailoring to specific electronic applications through integration and interdigitation of multiple structures. The results illustrate the diversity of possibilities through both the finite element method (FEM) and experimental demonstration. The approximate fractal dimensions in these finite-iterative curves range from 1.5 to 2. The elastic tensile strains achieved with these structures indicate that they are suitable for use in various stretchable devices, including the epidermal electronic platform, with key advantages over previously described layouts. The study also demonstrates the mechanics and electronics of Peano-based geometries, showing that the Peano curve provides a model system for examining the detailed mechanics of fractal-based motifs. The results indicate that Peano layouts with unit cells all oriented in the same way maximize the uniaxial stretchability along the unit cell direction. The 'half-and-half' Peano layout, which contains unit cells with alternating orientations, balances the maximum strain supported along the x