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...full if the CPPN output is greater than a threshold (here set to 0.1), otherwise the voxel is considered empty. The 3D voxel array is then processed by the surface-smoothing Marching Cubes algorithm (=-=Lorensen and Cline 1987-=-). A normal is provided for each vertex when visualizing the objects in OpenGL, a graphics technique that further smooths the surface. These two smoothing steps enable high-resolution CPPN objects to ...

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...erimented with additional functions (see Results). The evolution of the population of CPPN networks occurs according to the principles of the NeuroEvolution of Augmenting Topologies (NEAT) algorithm (=-=Stanley and Miikkulainen 2002-=-). The NEAT algorithm contains three major components (Stanley and Miikkulainen 2002). (1) It starts with small genomes that encode simple networks and complexifies them via mutations that add nodes a...

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...evelop (Wolpert and Tickle 2010, Bentley 1996). An example is Lindenmayer Systems (L-Systems), which iteratively replace symbols in strings with other symbols until a termination criteria is reached (=-=Lindenmayer 1968-=-, Hornby et al. 2003). While L-Systems can reproduce a wide variety of organismal shapes, especially those of branching plants, they do not model plant developmental processes (Wolpert and Tickle 2010...

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... (1994), who evolved morphologies that resembled some biological creatures, although with an abstract encoding based on parameterized recursion that does not resemble natural developmental processes (=-=Sims 1994-=-). A third option is possible, wherein a high-level abstraction is based on the developmental processes that give rise to natural forms. An example of this approach is Compositional Pattern Producing ...

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...Another useful regularity is repetition, which occurs frequently in the evolved objects (e.g. the top-right object in Figure 3). A further beneficial property is exhibiting regularity with variation (=-=Stanley and Miikkulainen 2003-=-, Lipson 2007, Clune et al. 2011). For example, Figure 4b1 has a motif that appears like an animal head, but is repeated in different sizes and with other subtle variations. Symmetric patterns with as...

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...is possible, wherein a high-level abstraction is based on the developmental processes that give rise to natural forms. An example of this approach is Compositional Pattern Producing Networks (CPPNs) (=-=Stanley 2007-=-), which are used to evolve 3D objects in this paper and are described in Methods. Two groups have previously evolved 3D objects with CPPNs, although neither conducted an openended exploration of 3D o...

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...The former camp frequently simulates the low-level processes that govern biological development, such as the diffusing morphogen chemicals and proteins that determine the identity of embryonic cells (=-=Bongard and Pfeifer 2001-=-, Eggenberger 1997, Miller 2004). While this approach facilitates studying the mechanisms of developmental biology, the computational cost of simulating chemistry in such detail greatly limits the com...

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...-level processes that govern biological development, such as the diffusing morphogen chemicals and proteins that determine the identity of embryonic cells (Bongard and Pfeifer 2001, Eggenberger 1997, =-=Miller 2004-=-). While this approach facilitates studying the mechanisms of developmental biology, the computational cost of simulating chemistry in such detail greatly limits the complexity of the evolved phenotyp...

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...of objects CPPNs can produce. Additionally, interactive evolution avoids the greedy nature of target-based evolution, potentially allowing it to access more interesting objects (Secretan et al. 2011, =-=Lehman and Stanley 2008-=-). A drawback of interactive evolution is that it is subjective, but science should not abandon such a useful tool simply because it is subjective. While user preferences bias the types of objects sel...

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...high-level abstractions that enable the evolution of more elaborate forms with many parts, but these abstractions tend not to reflect the way that organisms actually develop (Wolpert and Tickle 2010, =-=Bentley 1996-=-). An example is Lindenmayer Systems (L-Systems), which iteratively replace symbols in strings with other symbols until a termination criteria is reached (Lindenmayer 1968, Hornby et al. 2003). While ...

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...ct. To magnify differences in fitness values, all fitness scores serve as an exponent to a large constant c = 2000 to produce the final fitness value. The parameters are identical to a previous work (=-=Clune et al. 2011-=-), except mutations were allowed to be larger (MutationPower = 2.5). Results and Discussion Interactive Evolution Overall summary We study interactive evolution because it allows an open-ended explora...

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...d Tickle 2010, Bentley 1996). An example is Lindenmayer Systems (L-Systems), which iteratively replace symbols in strings with other symbols until a termination criteria is reached (Lindenmayer 1968, =-=Hornby et al. 2003-=-). While L-Systems can reproduce a wide variety of organismal shapes, especially those of branching plants, they do not model plant developmental processes (Wolpert and Tickle 2010). Another example i...

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...oth for studying morphological evolution and harnessing it for engineering or artistic purposes. The objects are frequently regular, a property which is important in engineering and for evolvability (=-=Lipson 2007-=-, Clune et al. 2011). An important regularity is symmetry, which is evident with respect to different dimensions in many of the objects. For example, all of the objects in generation 33 of Figure 3 ar...

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...adients provided have noticeable effects after a thousand generations. This result is in line with a previous paper that found that the information input into CPPNs can bias the resulting phenotypes (=-=Clune et al. 2009-=-). We include this input in the remaining treatments in this paper because it facilitates round surfaces, even though it hurt performance in this experiment. Because interactive evolution features sma...

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...ts with CPPNs, although neither conducted an openended exploration of 3D objects. One group evolved CPPN objects that were composed of variable-sized spheres and were evaluated on two tasks: falling (=-=Auerbach and Bongard 2010-=-b) or moving rapidly (Auerbach and Bongard 2010a). Most of the evolved forms resembled clubs. A second group evolved soft-bodied robots to move quickly (Hiller and Lipson 2010). These studies demonstr...

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...n two tasks: falling (Auerbach and Bongard 2010b) or moving rapidly (Auerbach and Bongard 2010a). Most of the evolved forms resembled clubs. A second group evolved soft-bodied robots to move quickly (=-=Hiller and Lipson 2010-=-). These studies demonstrate that CPPNs can create functional shapes, but leave open the question of what types of 3D objects CPPNs can produce with fewer constraints and without specific objectives. ...